Relationship of Data Word Size to Dynamic Range and Signal Quality in Digital Audio Processing Applications
 What Are the Benefits of Using a DSP to Process Audio Signals?
 DSP Numeric Data Formats: Do I Require Fixed or Floating Point Arithmetic For My Audio Application?
 The Relationship of Dynamic Range to Data Word Size in Digital Audio
 Considering Data Word Length Issues When Developing Audio Algorithms Free From Noise Artifacts
 Maintaining 16bit 'CDQuality' Accuracy During DSP Processing
 Processing 110120 dB, 20/24bit ProfessionalQuality Audio
 Summary of Data Word Size Requirements for Processing Audio Signals
 ADSP21161 SIMD SHARC DSP  The 32bit Processor of Choice for Present and Future Audio DSP
Appendix  References
Glossary for Some Common A/D and D/A Audio Converter Terms
Since the introduction of the compact disc in the early 1980s, digital technology has become the standard for the recording and storage of highfidelity audio. It is not difficult to see why. Digital signals are robust. Digital signals can be transmitted and copied without distortion. Digital signals can be played back without degrading the carrier. Who would want to go back to scraping a needle along a vinyl groove now?
Another advantage of digital audio signals is the ease with which they can be manipulated. Digital Signal Processing (DSP) technology has advanced to such an extent that almost any audio product, from a mobile phone to a professional mixing console, contains a DSP chip. Once again the reasons for the success of DSP are simple: stability, reliability, enhanced performance and programmability. Signal processing functions can be implemented for a fraction of the cost, and in a fraction of the space required by analog circuitry, as well as providing functionality that simply couldn't be done in analog. In fact, so ubiquitous has it now become that, for many people, the word "digital" has become synonymous with "high quality".
The everincreasing performance and falling cost of DSP hardware have generated new applications and new markets for digital audio in both the consumer and professional audio sectors. Digital Versatile Disk (DVD) and digital surround sound in the home, digital radio and handsfree cellular phones in the car are just a few of the DSPbased technologies which have appeared in the last few years. The demands on the quality, speed and flexibility of DSP has also increased as more functionality is added to DSP products: a DSP might now be required for mixing, equalization, dynamic range compression and data decompression, all in one product, implemented on one chip.
16bit, 44.1 kHz PCM digital audio continues to be the standard for high quality audio in most current applications such as CD, DAT, and highquality PC audio. Recent technological developments and improved knowledge of human hearing, however, have created a demand for greater data word lengths. Analogtodigital converters now available support 18, 20, and 24bits and are capable of exceeding the 96dB dynamic range available using 16bit data words. Many recording studios now routinely master their recordings using 20 or 24bit recorders. These technological developments are beginning to make their way into the consumer and "prosumer" audio applications. The most obvious consumer audio impact is DVD which is capable of carrying audio with up to 24bit resolution at sample rates well above 48 kHz. Another example is a 16channel digital home studio recorder, capable of sampling at a 96 kHz sample rate with 24bit resolution. In fact, three trends can be identified which have influenced the current generation of digital audio formats which are set to replace CD digital audio. These can be summarized as follows:
 Higher resolution  either 20 or 24bits per data word
 Higher sampling frequency  typically 96 kHz and 192 kHz
 More audio channels for a more realistic "3D" sound experience
Lowcost, higherperformance digital signal processors are now appearing on the market to satisfy the high dynamic range requirements for processing or synthesizing audio signals. How many bits are required for processing audio signals? Is it 16, 20, 24, or 32 bits? Does the audio application require fixedpoint of floatingpoint arithmetic? What undesirable side effects of quantization should the audio designer look out for?
The first section in this report briefly reviews desirable characteristics of a DSP for use in audio applications, and then discusses the differences in data formats for fixed and floatingpoint processors. Next, the relationship of dynamic range to data word size in processing audio signals is examined. This will aid in determining how many bits would be required for your application, whether it is a lowercost, lowfidelity consumer device or a highperformance, highfidelity professional audio gear. Finally, to design a system with either CDquality or professionalquality audio, it is suggested that for a digital filter routine to operate transparently, the resolution of the processing system must be considerably greater than that of the input signal. For the highestquality, professional audio systems, a 32bit DSP is offered as a suggested solution.
1. What are the Benefits of Using a DSP to Process Audio Signals?
A digital signal processor has one purpose: to operate on quantized signal data as quickly and efficiently as possible. Compared to a typical CPU or microcontroller, a wellarchitected DSP usually contains the following desirable characteristics to perform realtime DSP computations on audio signals:
Fast and Flexible Arithmetic
Singlecycle computation for multiplication with accumulation, arbitrary amounts of shifting, and standard arithmetic and logical operations.
Extended Dynamic Range for Extended Sumof Product Calculations
Extended sumsofproducts, common in DSP algorithms, are supported in multiplyaccumulate units. Extended precision in the multiplier's accumulator provides extra bits for protection against overflow in successive additions to ensure that no loss of data or range occurs.
Singlecycle Fetch of Two Operands For SumofProducts Calculations
In extended sumsofproducts calculations, two operations are needed on each cycle to feed the calculation. The DSP should be able to sustain twooperand data throughput, whether the data is stored onchip or off.
Hardware Circular Buffer Support For Efficient Storage and Retrieval of Samples
A large class of DSP algorithms, including digital filters, requires circular data buffers. A circular buffer is a finite segment of the DSP's memory defined by the programmer that is used to store samples for processing. Hardware Circular Buffering is designed to allow automatic address pointer wraparounds to the beginning of the buffer for simplifying circular buffer implementations, and thus reducing overhead and improving performance. When circular buffering is implemented in hardware, the DSP programmer does not have to be concerned with the additional overhead of testing and resetting the address pointer so that it does not go beyond the boundary of the buffer.
Efficient Looping and Branching for Repetitive DSP Operations
DSP algorithms are repetitive and are most logically expressed as loops. For digital filter routines, a running sum of MAC operations is typically executed in fast, efficient loop structures. A DSP's program sequencer, or control unit, should allow looping of code with minimal or zero overhead. Any loop branching, loop decrementing, and termination test operations are built into the DSP control unit hardware. Also, no overhead penalties should result for conditional branching instructions which branch based of a computation unit's status bits.
All of the above architectural features are used for implementation of DSPtype operations. For example, convolution is a common signal processing operation involving the multiplication of two sets of discrete data, an input multiplied with a shifted version of the impulse response to a system, and keeping a running sum of the outputs. This is seen in the following convolution equation [17, 18, 19, 20]:
DSP architectural features are designed to perform these types of discrete mathematical operations as quickly as possible, usually within a single instruction cycle. Examining this equation closely shows elements required for implementation. The filter coefficients and input samples required to implement the above equation can be stored in two memory arrays defined as circular buffers. Both circular buffers need to be multiplied together and added to the results of previous iterations. To perform the operation shown above, the DSP architecture should allow one multiplication to be executed, along with an addition to a previous result in a single instruction cycle. Within the same cycle, the architecture should also contain enough parallelism in the compute units to enable memory reads of the next sample and filter coefficient for the next loop iteration. Hardware looping circuitry included in the architecture would allow efficient looping through the number of iterations with zerooverhead. When used in a zerooverhead loop, digital filter implementations become extremely optimized since no explicit software decrement, test and jump instructions are required. Thus, for actual implementation of the convolution operation, two circular buffers, multipliers, adders, and a zerooverhead loop construct are required. A digital signal processor contains the necessary building blocks to accomplish implementation of discretetime filter operations.
In performing these types of repetitive DSP calculations, quantization errors from truncation and rounding can accumulate over time, degrading the quality of the DSP algorithmic result. The number of bits of resolution used in the arithmetic computations, along with a given filter structure realization, will determine the robustness of a filter algorithm's signal manipulation. The rest of this article will discuss how many bits would potentially be required for a particular audio application, as this is determined by the complexity of the processing and the desired target signal quality.
2. DSP Numeric Formats: Do I Required Fixed or Floating Point Arithmetic for my Audio Application?
Depending on the complexity of the application, the audio system designer must decide on how much computational accuracy and dynamic range will be needed. The most common native data types are explained briefly in this section. 16 and 24bit fixedpoint DSPs are designed to compute integer or fractional arithmetic. 32bit DSPs like the Analog Devices ADSP2106x SHARC family were traditionally offered as floating point devices, however, this popular family of DSPs can equally perform both floatingpoint arithmetic and integer or fractional fixedpoint arithmetic.
2.1 16, 24, and 32Bit FixedPoint Arithmetic
DSPs that can perform fixedpoint operations typically use a two's complement binary notation for representing signals. The representation of the fixedpoint format can be signed (twoscomplement) or unsigned integer or fractional notation. Most DSP operations are optimized for signed fractional notation. For example, the Analog Devices ADSP21161 is capable of 32bit fractional arithmetic.
The numeric format in signed fractional notation makes sense to use in DSP computations, because a fractional representation it would easily correspond to a ratio of the full range of samples produced from a 5 Volt A/D converter, as shown in Figure 1 below. It is harder to overflow a fractional result, because multiplying a fraction by a fraction results in a smaller number, which is then either truncated or rounded. The highest fullscale positive fractional number would be 0.99999, while the highest full scale negative number is 1.0. Anything in between the highest representable signal from the converter would be a fractional representation of the "loudest" signal. For example, the midway positive amplitude for a converter would be 1/2, and this would be interpreted as a fractional value of 0x4000 by the DSP.
Fig. 1. Signed Two's Complement Representation of Sampled Signals
Fig. 2. Fractional And Integer Formats for a Nbit number
In the fractional format, the binary point is assumed to be to the to the left of the LSB (sign bit). In the integer format, the binary point is to the right of the LSB (Figure 2).
Fractional math is more intuitive for signal manipulation, and it is the least significant bits in a fractional result that we will examine in this article, since it is in these lower order bits that can suffer from quantization errors due to finite word length effects. The more bits that are used to represent a given audio signal will produce a more accurate arithmetic result. This is discussed in Section 3.
2.2 32/40bit FloatingPoint Arithmetic
Floating point math offers flexibility in programming because it is much harder to overflow a result, while the programmer is less concerned about scaling inputs to prevent overflow. IEEE 754/854 Floatingpoint data is stored in a format that is 32 bits wide, where 24 bits represent the mantissa and 8 bits represent the exponent. The 24bit mantissa is used for precision while the exponent is for extending the dynamic range. For 40bit extended precision, 32 bits are used for the mantissa while 8 bits are used to represent the exponent (figures 3 and 4).
Fig. 3. IEEE 754/854 32Bit Single Precision FloatingPoint Forma
A 32bit floating point number is represented in decimal as:
Its binary numeric IEEE format representation is stored on the 32bit floating point DSP as:
It is important to know that the IEEE standard always refers to the mantissa in signedmagnitude format, and not in twoscomplement format. So the extra hidden bit effectively improved the precision to 24 bits and also insures any number ranges from 1 (1.0000E00) to 2 (1.1111E11) since the hidden bit is always assumed to be a 1.
Fig. 4. 40Bit Extended Precision FloatingPoint Format
Figure 7 shows the 40bit extended precision format available that is also supported on the ADSP2106x family of DSPs. With extended precision, the mantissa is extended to 32 bits. In all other respects, it is the same format as the IEEE standard format. 40bit extended precision binary numeric format representation is stored as:
For audioprocessing, the dynamic range of floating point may be unnecessary for some algorithms, but the flexibility in programming in floatingpoint make it desirable to take advantage of, especially for highlevel programming languages like C. Keep in mind, that many of the fixedpoint precision issues discussed in later sections would still apply for a DSP that supports floating point arithmetic, at least in terms of truncation and coefficient quantization. The programmer still has to convert the fixedpoint data coming from an A/D converter to it's floating point representation, while the floatingpoint result has to be converted back to it's fixedpoint equivalent when the data is sent to a D/A converter.
Floatingpoint arithmetic was traditionally used for applications that have very high dynamic range requirements, like image processing, graphics and military/space applications. The dynamic range offered for 32bit IEEE floatingpoint arithmetic is 1530 dB. Typically in the past, tradeoffs were considered with price vs. performance when deciding on the use of floatingpoint processors. Until recently, the higher cost made 32bit floating point DSPs unreasonable for use in audio. Today, designers can achieve highquality audio using either 32bit fixed or floating point processing with the introduction of the lowercost 32bit processors like the ADSP21161, at a cost comparable to 16bit and 24bit DSPs.
3. The Relationship of Dynamic Range to Data Word Size in Digital Audio
One of the top considerations when designing an audio system is determining acceptable signal quality for the application. Table 1 below shows some comparisons of signal quality for some audio applications, devices and equipment [13].
Table 1. Dynamic Ranges
Audio Device/Application  Dynamic Range 
AM Radio 
48 dB 
Analog Broadcast TV 
60 dB 
FM Radio 
70 dB 
Analog Cassette Player 
73 dB 
Video Camcorder 
75 dB 
ADI SoundPort Codecs 
80 dB 
16bit Audio Converters 
90 to 95 dB 
Digital Broadcast TV 
85 dB 
MiniDisk Player 
90 dB 
CD Player 
92 to 96 dB 
18bit Audio Converters 
104 dB 
Digital Audio Tape (DAT) 
110 dB 
20bit Audio Converters 
110 dB 
24bit Audio Converters 
110 to 120 dB 
Analog Microphone 
120 dB 
Audio equipment retailers and consumers often use the phrase 'CDquality sound' when referring to high dynamic range audio. Compare sound quality of a CD player to that of an AM radio broadcast. For higher quality CD audio, noise is not audible, especially during quiet passages in music. Lower level signals are heard clearly. But, the AM radio listener can easily hear the low level noise at very audible levels to where it can be a distraction to the listener. With an increase of an audio signal's dynamic ranges, then better distinction one can make for lowlevel audio signals while the noise floor is lowered and becomes undetectable to the listener ("noise floor" is a term used to describe the point where the audio signal cannot be distinguished from lowlevel white noise).
"Recent advancements within the past decade in human hearing indicate the sensitivity of the human ear is such that the dynamic range between the quietest sound detectable and the maximum sound which can be experienced without pain is approximately 120dB. Further studies suggest there is critically important audio information at frequencies up to 40 kHz and possibly 80 kHz"
To achieve CDtype signal quality, the trend in recent years has been to design a system that processes audio signals digitally, using 16bit A/D and D/A converters signaltonoise ratio (SNR) and dynamic range around 9093 dB. When processing these signals, the programmer should normally design the algorithm with enough computation precision that is usually greater than 16bits in compact disk signals. CDquality audio is just one example. For whatever the application, the audio system designer must first determine what is an acceptable SNR and then decide how much precision is required to produce acceptable results for the intended application.
3.1 What Is The SNR and Dynamic Range for a DSP?
In analog and digital terms, SNR (S/N ratio) and dynamic range often used synonymously. In pure analog terms, SNR is defined as the ratio of the largest known signal that exists to the noise present when no signal exists. In digital terms, SNR and dynamic range are used synonymously to describe the ratio between the largest representable number to the quantization error [2]. A welldesigned digital filter should contain a maximum signal to noise ratio (SNR) that is greater than the converter SNR. Thus, the DSP designer must be sure that the noise floor of a filter is not larger than the minimum precision required of the ADC or DAC.
Figure 5 below shows the relationship between dynamic range, SNR and headroom:
Fig. 5. Audio Signal Level (dBu) Relationship Between Dynamic Range, SNR and Headroom
Here is a summary of the terms shown in the figure 9 as defined by Davis and Jones [3] (we will be referring to many of these terms frequently throughout this article):
Decibel  Used to describe sound level (sound pressure level) ratio, or power and voltage ratios:
dBVolts=20log(Vo/Vi), dBWatts=10log(Po/Pi), dBSPL=20log(Po/Pi)
Dynamic Range  The difference between the loudest and quietest representable signal level, or if noise is present, the difference between the loudest (maximum level) signal to the noise floor. Measured in dB.
Dynamic Range = (Peak Level)  (Noise Floor) dB
SNR (SignalToNoise Ratio, or S/N Ratio)  The difference between the nominal level and the noise floor. Measured in dB. Other authors define this for analog systems as the ratio of the largest representable signal to the noise floor when no signal is present[6], which more closely parallels SNR for a digital system.
Headroom  The difference between nominal line level and peak level where signal clipping occurs. Measured in dB. The larger the headroom, the better the audio system will handle very loud signal peaks before distortion occurs.
Peak Operating Level  The maximum representable signal level at which point clipping of the signal will occur.
Line Level  Nominal operating level ( 0 dB, or more precisely between 10 dB and +4 dB)
Noise Floor  The noise floor for human hearing is the average level of 'just audible' white noise. Analog audio equipment can generate noise from components. With a DSP, noise can be generated from quantization errors. [One can make an assumption that the headroom + S/N ratio of an electrical analog signal equals the dynamic range (although not entirely accurate since signals can still be audible below the noise floor)].
"In theoretical terms, there is an increase in the signaltoquantization noise or dynamic range by approximately 6 dB for each bit added to the wordlength of an ADC, DAC or DSP."
In "realworld" signal processing, quantization is the process by which a number is approximated by a number of finite precision. For example, during analogtodigital conversion, an infinitely variable signal voltage is represented by a binary number with a fixed number of bits. The difference between two consecutive binary values is called the quantization step, or quantization level. The size of the quantization step defines the effective noise floor of the quantized signal. The word length for a given processor determines the number of quantization levels that are available. For an nbit data word would yield 2n quantization levels (some examples for common data word widths are shown in Table 2).
Table 2: An nbit data word yields 2n quantization levels
N Quantization Levels for nbit data words ( N = 2n levels) 
28 = 256 
216 = 65,536 
220 = 1,048,576 
224 = 16,777,216 
232 = 4,294,967,296 
264 = 18,446,744,073,729,551,616 
The higher number of bits used to represent a sample will result in a better approximation of the audio signal and a reduction in quantization error (noise), which produces and an increase in the SNR. In theoretical terms, there is an increase in the signaltoquantization noise or dynamic range by approximately 6 dB for each bit added to the word length of an ADC, DAC or DSP.
Fig. 6. DSP/Converter SNR and Dynamic Range
Note that the "6dBPerBitRule" is an approximation to calculating the actual dynamic range for a given word width. The maximum representable signal amplitude to the maximum quantization error for of an ideal A/D converter or DSPbased digital system is actually calculated as:
1.76 dB is based on sinusoidal waveform statistics, and would vary for other waveforms, and n represents the data word length of the converter or the digital signal processor [9].
In undithered DSPbased systems, the SNR definition above is not directly applicable since there is no noise present when there is no signal. In digital terms, dynamic range and SNR (Figure 6) are often both used synonymously to describe the ratio of the largest representable signal to the quantization error or noise floor [2]. Therefore, when referring to SNR or dynamic range in terms of DSP data word size and quantization errors  both terms mean the same thing.
Now the question arises, how many bits are required to design a high quality audio system? In terms of dynamic range and SNR, what is the best precision one can choose without sacrificing low cost in a given design? Let's first see what are the dynamic range comparisons between DSPs with different native data word sizes. Figure 7 shows the dynamic range relationship between the three most common DSP fixedpoint processor dataword width: 16, 24 and 32bits. The quantization level comparisons are also given. As stated earlier, the number of dataword bits used to represent a signal directly affects the SNR and quantization noise introduced during the sample conversions and arithmetic computations.
Fig. 7. FixedPoint DSP Dynamic Range Comparisons
Table 3. Dynamic Range Vs. Resolution
Precision (FixedPoint Binary Representation)  Dynamic Range (# of bits per data word x 6 db/bit or resolution) 
16bit 
96 dB 
24bit 
144 dB 
32bit 
192 dB 
Each additional bit of resolution that is used by the DSP for calculations will reduce the quantization noise power by 6dB. 16bit fixedpoint numeric precision yields 96 dB [16 x 6dB per bit], 24bit fixedpoint precision yields 144 dB [24 x 6dB per bit], while 32bit fixedpoint precision will yield 192 dB [32 x 6dB per bit]. Note that for native singleprecision math, a 16bit DSP is not adequate for accurately representing the full dynamic range required for 'higherfidelity' audio signals around 120 dB.
In terms of quantization levels, figure 8 demonstrates how 32bit and 24bit processing can more accurately represent a processed audio signal as compared to 16bit processing. 24bit processing can more accurately represent a signal 256 times better than 16bit processing, while 32bit processing can more accurately represent signals 65,536 times better than that for 16bit processing, and 256 times more accurately than that of a 24bit processor.
Fig. 8. Fixed Point DSP Quantization Level Comparisons
Using the "6dBPerBitRule," 32bit IEEE floating point dynamic range is determined to be 1530 dB. For floating point this is calculated by the size of the exponent  6 dB x 255 exponent levels = 1530 dB. (255 levels come from the fact that there is an 8bit exponent). For floatingpoint audio processing, we can see there is much more dynamic range available than the 120 dB required for covering the full audio dynamic range capabilities of the human ear.
3.2 Additional Fixed Point MAC Unit Dynamic Range for DSP Overflow Prevention
Computation overflow/underflow is a hardware limitation that occurs when the numerical result of the fixedpoint computation exceeds the largest or smallest number that can be represented by the DSP. Many DSPs include additional bits in the MAC unit to prevent overflow in intermediate calculations. Extended sumsofproducts, which are common in DSP algorithms, are achieved in the MAC unit with single cycle multiply accumulates placed in an efficient loop structure. The extra bits of precision in the accumulator result register provide extended dynamic range for the protection against overflow in successive multiplies and additions. Thus, no loss of data or range occurs. Table 4 shows a comparison of the extended dynamic ranges of 16bit, 24bit, and 32bit DSPs. Note that the ADSP21161 SHARC 32bit DSP has a much higher extended dynamic range than 16 and 24bit DSPs when executing fixedpoint multiplication instructions. The MAC unit on the SHARC contains dual accumulators that can produce an 80bit fixedpoint result when multiplying two 32bit fixed point values. There are 16 bits of additional precision for the 64bit MAC result. The SHARC's 80bit result can yield a fixedpoint dynamic range as high as 480 dB for intermediate calculations.
Table 4. Comparison of Extended Dynamic Range in FixedPoint DSP Multiplier Unit
Nbit DSP  Nbit x Nbit Multiply 
Additional MAC Result Bits 
Precision in MAC Result Register 
Additional Dynamic Range Gained 
Resulting MAC Dynamic Range 
16bit DSP  32bit 
8bit 
40bit 
48 dB 
240 dB 
24bit DSP 
48bit 
8bit 
56bit 
48 dB 
336 dB 
32bit SHARC 
64bit 
16bit 
80bit 
96 dB 
480 dB 
4. Considering Data Word Length Issues When Developing Audio Algorithms Free from Noise Artifacts
Digital Signal Processing is often discussed as if the signals to be processed and the filter arithmetic used to process them are both of infinite precision. However, all implementations of DSP necessarily use words of finite length to represent each and every value, be it a digital audio input sample, a filter coefficient or the result of a multiplication. This finite precision of representation means that any digital signal processing performed to generate a desired result introduces inaccuracy into the result. If a signal goes through several stages of DSP, then each stage will add more inaccuracy.
The effects of a finite word length can severely effect signal quality (i.e. lower the system S/N ratio) and produce unacceptable error when performing DSP calculations. Undesirable effects of finite precision can result of any of the following:
 A/D Conversion Noise
Finite precision of an input data word sample will introduce some inaccuracy for the DSP computation as a result of the nonlinearities inherent in the A/D Conversion Process. Therefore, the accuracy of the result of an arithmetic computation can not be greater than the resolution of the quantized sample. In other words, the A/D conversion process will establish the noise floor for the DSP (unless the D/A converter has a lower noise floor). The DSP programmer must ensure that the noise floor of the processing algorithm does not exceed the noise floor of the A/D converter.
 Quantization Error of Arithmetic Computations From Truncation and Rounding
DSP Algorithms such as Digital Filters will generate results that must be truncated or rounded up (i.e. requantized). When a processing result need to be stored, it must be quantized to the native dataword length of the processor, introducing an error. For recursive DSP algorithms these requantized values are part of a feedback loop, causing arithmetic errors can build up, which then reduces the dynamic range of the filter. The smaller the data word of the DSP, the more likely these types of errors will show up in the DA converted output analog signal.
In a nbit fixedpoint system, quantization of results may be considered as the addition of noise to the result. Consider a multiplication operation in a digital filter, including requantization of the result. This can be modeled as an infiniteprecision multiplication followed by an addition stage where quantization noise is added to the product so that the result is equal to a nbit number [15].
In a digital signal processing system multiplication, addition and shift operations are performed on a sequence of nbit input values. These operations generate results which would require more than n bits to be represented accurately. The solution to this problem is generally to eliminate the loworder bits resulting from an arithmetic operation in order to produce a nbit value which can be stored by the system.
The two most common methods for eliminating the loworder bits are truncation and rounding. Truncation is accomplished by simply discarding all bits less significant than the least significant bit that is retained. Rounding is performed by choosing the nbit number which is closest to the original unrounded quantity.
 Computational Overflow
Whenever the result of an arithmetic computation is larger than the highest positive or negative fullscale value, an overflow will occur and the true result will be lost.
 Coefficient Quantization
Finite Word Length (nbit data word size) of a filter coefficient can affect pole/zero placement and a digital filter's frequency response. This imprecision can cause distortion in the frequency response of the filter and, in the worst case, instability.
Errors in the values of a filter's coefficients cause alterations in the positions of the transfer function poles and zeros and therefore are manifested as changes to the frequency and phase response characteristics of the filter. In a DSP system of finite precision, such deviations cannot be avoided. It can, however, be reduced by using greater precision for the representation of coefficients. This issue is particularly important for poles close to the unit circle in the zplane, where an inaccuracy could make the difference between stability and instability.
Limit Cycles
Occur in IIR filters from truncation and rounding of multiplication results or addition overflow. These often cause periodic oscillations in the output result, even when the input is zero.
Other than A/D Conversion Noise, all other effects of having a finite dataword size are mainly dependent on the precision of the requantization of data and the type of arithmetic operations used in the DSP algorithm. Any given filter structure can offer a significantly lower noise floor over another structure which accomplishes the same task.
"The overall DSPbased audio system dynamic range is only as good as it's weakest link."
In a DSPbased audio system, this means that any one of the following sources or devices in the audio signal chain will determine the dynamic range of the overall audio system [9]:
 The "real world" analog input signal, typically from a microphone or linelevel source
 The A/D converter word size and conversion errors
 DSP finite word length effects such as quantization errors resulting from truncation and rounding, and filter coefficient quantization
 The D/A converter word size
 The analog output circuitry connecting to a speaker
 or, another device in the signal path that will further process the audio signal
So the choice of components and the digital filter implementation will also determine the overall quality of the processed signal. For example, if we have a 75 dB D/A converter and a DSP which can maintain 144 dB dynamic range, the overall 'System' dynamic range will still only be 75 dB. So the D/A converter is the limiting factor. Even thought the DSP would compute a given algorithm and maintain a result that had 122 dB of precision and dynamic range, the result would have to be truncated in order for the DAC to properly convert it back to an analog signal. Now, if the choice is made to high quality analog, ADC, and DAC components, wouldn't one want to be careful to ensure the signal quality is maintained by the DSP algorithm? Care must then be taken in a digital system to ensure the DSP is not the weakest chain in the 'signal chain'.
"For a digital filter routine to operate transparently, the resolution of the processing system must be considerably greater than that of the input signal so that any errors introduced by the arithmetic computations are smaller than the precision of the ADC or DAC."
If a digital signal processing algorithm produces quantization noise artifacts which are above the noise floor of the input signal, then these artifacts will be audible under certain circumstances, especially when an input signal is of low intensity or limited frequency. Therefore, whatever the dynamic range of a highquality audio input, be it 16, 20 or 24bit input samples, the digital processing which is performed on it should be designed to prevent processing noise from reaching levels at which it may appear above the noise floor of the input, and thus become audible content [see 2Wilson and 5Chen]. For a digital filter routine to operate transparently, the resolution of the processing system must be considerably greater than that of the input signal so that any errors introduced by the arithmetic computations are smaller than the precision of the ADC or DAC. In order for the DSP to maintain the SNR established by the A/D converter, all intermediate DSP calculations require the use of higher precision processing greater than the input sample wordsize [see 2Wilson, 3Dattorro, 4Zolzer, 5Chen, 6Kloker, Lindsley & Thompson].
What are the dynamic ranges that must be maintained for CDquality and Professionalquality audio designs? Fielder [9] demonstrated the dynamic range requirements for consumer CD audio requires 16bit conversion/processing while the minimum requirement for professional audio is 20bits (based on perceptual tests performed on human auditory capabilities). Traditional dynamic range application requirements for highfidelity audio processing can be categorized into two groups:
'Consumer CDQuality' audio systems uses 16bit conversion with typical dynamic ranges between 8593 dB.
'ProfessionalQuality' audio systems uses 2024 bit conversion with dynamic ranges between 110122 dB.
5. Maintaining 16bit 'CDQuality' Accuracy During DSP Processing
As we saw in the last section, when using a DSP to process audio signals, the DSP designer must ensure that any quantization errors introduced by the arithmetic calculations executed on the processor are lower than the converter noise floor. Consider a 'CDquality' audio system. If the DSP is to process audio data from a 16 bit A/D converter (ideal case), a 96 dB SNR must be maintained through the algorithmic process in order to maintain a CDquality audio signal (6x16=96dB). Therefore, it is important that all intermediate calculations be performed with higher precision than the 16bit ADC or DAC resolution [6]. Errors introduced by the arithmetic calculations can be minimized when using larger dataword width sizes for processing audio signals. For fractional fixedpoint math, we can visualize the addition of extra 'footroom' bits added to the right of the least significant bit of the input sample. The larger word sizes used in the arithmetic operations will ensure that truncation or roundoff errors will be lower than the noise floor of the D/A converter, as long as 'optimal' algorithms (better filter structures) are utilized in conjunction with the larger word width.
When considering selection of a processor for implementation, a choice therefore has to be made. Should one use a lower dataword DSP using double precision math, or should a higher dataword DSP be used supporting single precision math, which is more efficient? It is estimated that doubleprecision math operations can take up to 45 times the overhead of single precision math [5, 6]. Doubleprecision not only adds computation overhead to a digital filter, it also doubles the memory storage requirements for the filter coefficient buffer and the input delay line buffer. Every application is different, and although some applications may suffice smaller native dataword width processor, the use of doubleprecision computations, coefficients and intermediate storage comes at the expense of a drastic reduction in processing throughput.
To visually see the benefits of a larger DSP word size, let's take a look at the processing of audio signals from a 16bit A/D converter that has a dynamic range close to it's theoretical maximum, in this case with a 92 dB signaltonoise ratio (see Figure 9 below). Figure 10 below shows a conceptual view of a 16bit data word that is transferred from an A/D converter to the DSP's internal memory. Typically, the data transfer would occur through a serial port interface from the serial A/D converter, and the DSP may be configured to automatically perform a direct memory transfer (DMA) of the sample at the serial port circuitry to internal memory for processing. Notice that for the 24bit and 32bit processors, there are adequate 'footroombits' below the noise floor (to the right) to protect against quantization errors.
Fig. 9. FixedPoint DSP Noise Floor with a typical 16bit ADC/DAC at 92 dB
Fig. 10. 16bit A/D Samples at 96 dB SNR
The 16bit DSP has 4 dB higher SNR than the A/D converter's 92 dB, so not much room for error would be allowed in arithmetic computations. We can easily see that for moderate to complex audio processing using single precision arithmetic, the 16bit DSP data path will not be adequate for precise processing of 16bit samples as a result of truncation and roundoff errors that can accumulate during the execution of the algorithm. As shown in the Figure 11, errors resulting from the arithmetic computations can easily be seen by the output D/A converter and thus become audible noise. For example, complex recursive computations can easily result in the introduction of 18 dB of quantization noise, and with the 16bit DSP word width, the errors are seen by the DAC and hence will be easily heard by the listener.
Fig. 11. 16bit D/A Output Samples with Finite Length Effects
Doubleprecision math can obviously still be used for the 16bit DSP if software overhead is available, but the real performance of the processor will be compromised. A 16bit DSP using singleprecision processing would only suffice for lowcost audio applications where processing is not too complex and SNR requirements are around 75 dB (audiocassette quality).
The same algorithm implemented on a 24bit or 32bit DSP would ensure these errors are not seen by the D/A converter. As can be seen in the figure 11, even though 18 dB of quantization noise was introduced by the computations in the 24bit and 32bit DSP, they remain well below the noise floor of the 16bit DAC when these two processors run the exact same algorithm.
The 24bit DSP has 8 bits below the converter noise floor to allow for errors. In other words, we have 8 digits to the right of the least significant bit in the 16bit input sample. It takes 256 multiplicative processing operations to be performed before the noise floor of the algorithm goes above the resolution of the input sample.
A 32bit DSP (e.g. the ADSP21161) has 16bits below the noise floor when executing 32bit fractional math, allowing for the greatest computation flexibility in developing stable, noisefree audio algorithms. There are 16 digits to the right of the least significant bit in the 16bit input sample. It would take 65,536 multiplicative processing operations before the noise floor of the algorithm would go above the resolution of the 16bit input. With more room for quantization errors, filter implementation restrictions seen with 16 or 24bit DSPs are now removed.
So, the higher number of bits used to process an audio signal will result in a reduction in quantization error (noise). If these errors remain below the noise floor, the overall 'digital system SNR' established by the converters is therefore maintained. The DSP should not the limiting factor in signal quality! When using a 16bit converter for 'CDquality' audio, the general recommendation widely accepted is to use a higher resolution processor (24 or 32bit) since additional bits of precision gives the DSP the ability to maintain the 96dB SNR of the audio converters [2, 5, 9].
5.1 Is 24Bit Processing Always Enough For Maintaining 16bit Sample Accuracy?
Now it would appear in some cases, 32bit processing would be unnecessary for minimal processing of 16bit data. In order to maintain a 96dB dynamic range, 24 bits would appear to be sufficient to process a 16bit signal without any doubleprecision math requirement. But the question is then asked: Is a 24bit DSP sufficient in all cases to guarantee that noise introduced in a DSP computation will never go above a 16bit noise floor? For moderate and nonrecursive DSP operations, 24bits should normally be sufficient. However, research conducted in recent years has clearly shown that for precise processing of 16bit signals in recursive audio processing, a 24bit DSP may not be sufficient. Recursive filters are necessary for a wide variety of audio applications such as graphic equalizers, parametric equalizers, and comb filters.
In a 1993 AES Journal publication, R. Wilson [2] demonstrated that even for recursive secondorder IIR filter computations on a 24bit DSP, the noise floor of the digital filter can still go above that of the 16bit sample and hence become audible. To compensate for this the use of error feedback schemes (error spectrum shaping) or doubleprecision arithmetic were recommended, especially for extremely critical frequency response designs. The use of doubleprecision math can add processor computational overhead by more than a factor of five in the filter computations, while doubling memory storage requirements.
Another March 1996 AES Journal publication by W. Chen [5] came to the same conclusion. In order to maintain the 96dB signaltonoise ratio for 24bit processing of secondorder IIR filters, a doubleprecision filter structure was required to ensure that the digital equalizer output's noise floor was greater than 96 dB. Chen researched various secondorder realizations to determine the best structure when performing 24bit processing on 16bit input. In one test case, he implemented a single highpass secondorder filter using directform1 structures, finding these implementations to yield an SNR between 85 to 88 dB, which is lower than the 96 dB theoretical maximum of the ideal 16bit A/D converter.
Chen's second example consisted of cascading of secondorder structures to implement a sixteenthorder digital equalizer. He then measured the noise floor of the equalizer using an Audio Precision System One tester in order to find an adequate secondorder IIR filter structure to meet his target 96dB requirement. The results of using the 24bit DSP on a 16bit sample are shown in Table 5.
Table 5. Chen's Results of 24bit 2nd Order IIR Processing on 16bit Data [March 1996 Journal of AES]
SecondOrder Filter Structure 
S/N Ratio (dB) Results for 16thorder Equalizer 
Cascaded Form 
1 75 dB 
Cascaded Form 
2 63 dB 
Cascaded Transposed Form 
1 70 dB 
Double Precision Cascaded Form 1 
100 dB 
Parallel Form 1 
85 dB 
Parallel Transposed Form 1 
79 dB 
Chen's conclusion  in order to maintain a higher signaltonoise ratio greater than 96 dB when cascading multiple secondorder stages, doubleprecision arithmetic was required. In his optimal implementation of the doubleprecision directform1 filter, there was an increase in the number of instruction cycles (3x increase) and greater memory space (2x increase) for storing internal filter states.
Recall that with a 32bit DSP, there are 8 extra bits of precision compared to a 24bit processor. For a given secondorder filter structure implemented on a 24bit processor is then implemented in a 32bit fixedpoint processor, the arithmetic result should result in a reduction in the noise floor by 48 dB. Directform 1 filter structures are generally the best filter structure for use in audio, because of better noise performance it provides [2, 3]. For example, we can see that in Chen's results (Table 5), the Parallel Form 1 structure used to construct the equalizer provided the best result for singleprecision 24bit computation. However, this is still less than the ideal 96dB case. The 24bit processor's 144dB ideal noise floor is significantly raised by 70 to 80 dB and as a result, it is greater than the 16bit converter's noise floor. If this same algorithm is implemented on a 32bit fixedpoint processor, the noise floor of the filter output is lowered by 48 dB (with the 8 extra 'footroom' bits) to 133 dB. This is not only sufficient for remaining lower than a 16bit converter's noise floor, but a 32bit implementation of the singleprecision directform 1 structure would be adequate for even a 24bit converter's noise floor as well.
When processing of 16bit samples with a 32bit processor versus a 24bit processor, the 8 additional bits available below the noise floor and the use of 32bit filter coefficients will ensure that doubleprecision overhead is not necessary when using any standard secondorder IIR filter realization.
6. Processing 110120 dB, 20/24bit ProfessionalQuality Audio
When the compact disc was launched in the early 1980s, the digital format of 16bit words sampled at 44.1 kHz, was chosen for a mixture of technical and commercial reasons. The choice was limited by the quality of available analogtodigital converters, by the quality and cost of other digital components, and by the density at which digital data could be stored on the medium itself. It was thought that the format would be sufficient to record audio signals with all the fidelity required for the full range of human hearing. However, research since the entrance of CD technology has shown that this format is imperfect in some respects.
New research conducted within the last decade indicates that the sensitivity of the human ear is such that the dynamic range between the quietest sound detectable and the maximum sound which can be experienced without pain is approximately 120dB. Therefore, 16bit CDquality audio is no longer thought to be the highestquality audio that can be stored and played back. Also, many audiophiles claimed that CDquality audio lacked a certain warmth that a vinyl groove offered. This may have been due to a combination of the dynamic range limitation of 16bits as well as the chosen sample rate of 44.1 kHz. The 16bit words used for CD allow a maximum dynamic range of 96 dB although with the use of dither this is reduced to about 93 dB. Digital conversion technology has now advanced to the stage where recordings with a dynamic range of 120dB or greater may be made, but compact disc is unable to accurately carry them[14].
Recent technological developments and improved knowledge of human hearing have created a demand for greater word lengths and faster sampling rates in the professional and consumer audio sectors. It has long been assumed that the human ear was capable of hearing sounds up to a frequency of about 20 kHz and was completely insensitive to frequencies above this value. This assumption was a major factor in the selection of a 44.1 kHz sampling rate. New research has suggested that many people can distinguish the quality of audio at frequencies of up to 25 kHz, and that humans are also sensitive to a degree to frequencies above even this value. This research is mainly empirical, but would mean that a substantially higher sampling frequency is necessary. D. E. Blackmer [7] has suggested that in order to fully meet the requirements of human auditory perception, a sound systems must be designed to cover the frequency range to up to 40 kHz (and possibly up to 80 kHz) with over 120 dB dynamic range to handle transient peaks. This is beyond the requirements of many of today's digital audio systems. As a result, 18, 20 and even 24 bit analogtodigital converters are now widely available which are capable of exceeding the 96dB dynamic range available using 16 bits.
6.1 The Race Toward The Use of 24bit A/D and D/A Conversion
Multibit SigmaDelta Converters capable of 24bit conversion are now in production by various manufacturers (Analog Devices, Crystal Semiconductor, and AKM Semiconductor to name a few). The popularity of 24bit D/A converters is increasing for both professional and highend consumer applications. The reason for using these higher precision AD and DA converters for audio processing is clear: the distortion performance (linearity) of these higher resolution converters are much better than 16bit converters. The other obvious reason is the increase in SNR and dynamic range that they provide over 1620 bit technology.
"24bit A/D and D/A converter technology is capable of 120122 dB dynamic range, fully supporting the dynamic range capability of the human ear up to the threshold of pain of 120 dB, at sample rates of 96 kHz and 192 kHz."
Many 24bit converters on the market range from 110 to 120 dB, which is professional quality and close to the range capable by the human ear. The higherend converters range from 117 dB to 122 dB (Conversion errors such as intermodulation distortion introduced by the 24bit converters limit the final SNR from the theoretical 148 dB maximum). These newer 24bit converters have up to 120122 dB dynamic range, easily allowing input sources such as a 120 dB lownoise condenser microphone.
At many AES conventions in recent years, professional equipment manufacturers have showcased equipment with 24bit conversion with 96 kHz sample rates. New DVD standards are extending the digital formats to 24bits at sample rates of 96 kHz and 192 kHz formats. Professional quality audio is emerging in consumer audio market sector, traditionally a market with less stringent audio specifications. The race is on for audio equipment manufacturers to include 24bit, 96 kHz converters to maintain signal quality up to 120 dB.
6.2 Comparing 24bit and 32bit Processing of Audio Signals with 24bit Resolution
For years it has been widely accepted that in most cases 24bit DSP processing offers adequate precision for 16bit samples. With higherprecision 24bit converters emerging to support newer professional and consumer audio standards, what will become the recommended processor wordwidth required to maintain 24bit precision? For 24bit conversion, a 24bit DSP may no longer be able to adequately process 24bit samples without resorting to doubleprecision math, especially for recursive secondorder IIR algorithms. Newer 24bit converter technology is making a strong case for 32bit processing. The use of a 32bit DSP has already become the logical processorofchoice for many audio equipment manufacturers when using a 24bit signal conversion. Let's examine why this is the case.
Figure 12 visually demonstrates a typical situation that can result from moderately complex or recursive processing of 24bit samples. Note that the 24bit sample in this case is assuming a 1.23 fractional number interpreted from the 24bit converters. The extra bits of precision that 32bit fixedpoint processing provides to the right of the 24bit input's LSB. For example, the parallel combination of secondorder IIR filters can result in significant quantization artifacts from in the lower order bits of the data word. If both the 24bit and 32bit end up producing errors that result in an introduction of 24 dB of noise (4 bits x 6 dB/bit), the error will show up on the 24bit DAC since the 24bit DSP has the result above the noise floor. Singleprecision computations with 24bit processing can limit the result of a processed input to about 15bit accuracy. Should one use double precision routines on the 24bit processor, or should one opt for a 32bit processor when using a 24bit converter? Using a 32bit processor, the errors produced during the computations will never be seen by a 120 dB, 24bit DA converter.
Fig. 12. 24bit D/A Output Samples with Finite Length Effects
Recall in section 5, analysis of Wilson's and Chen's research demonstrated that for even secondorder IIR filter designs using a 24bit processor, one may require the use of additional error feedback computations or doubleprecision math to ensure the noise floor remains lower that a 16bit converter. If 24bit computations can introduce noise artifacts that can go above a 16bit noise floor for complex second order filters, what does that mean? We can conclude that a 24bit DSP processing 24bit samples will result in the noise floor of the digital filter to always be greater than the 24bit converter's noise floor, unless methods are implemented to reduce the digital filter's noise floor. These costly methods of implementing errorfeedback schemes and doubleprecision arithmetic are unavoidable and can add significant overhead in processing of 24bit audio data.
With many converter manufacturers introducing 24bit A/D and D/A converters to meet emerging consumer and professional audio standards, the audio systems using these higher resolution converters will require at least 32bit processing in order to offer sufficient precision to ensure that a filter algorithm's quantization noise artifacts will not exceed the 24bit input signal. If optimal filter routines are used for complex processing, any quantization noise introduced in the 32bit computations will never be seen by the 24bit output DA converter. In many cases, the audio designer can choose from a number of secondorder structures because the result will still be greater than 120 dB. 32bit processing will guarantee that the noise artifacts remain below the 120dB noise floor, and hence provide a dynamic range of the audio signal up the human ear's threshold of pain. Therefore, the goal of developing robust audio algorithms is accomplished, and the only limiting factor when examining the signal quality (SNR) of the digital audio system is the precision of the 24bit A/D and D/A converters.
7. Summary of Data Word Size Requirements for Processing Audio Signals
To maintain high audiosignal quality well above the noise floor, all intermediate DSP calculations should be done using higher precision than the bit length of the quantized input data. High precision storage should also be used between the DSP's memory and computation units. The use of "optimal" filter algorithms, higher precision filter coefficients, and higher precision storage of intermediate samples (available with extended precision in the MAC unit) will ensure that errors introduced by the arithmetic computations are much smaller than the error introduced by the conversion of the results by a DAC. Therefore, the noise floor of the digital filter algorithm will be lower than the resolution of the A/D and D/A converters.
A 16bit DSP may suffice for low cost audio applications where processing is not complex and SNR requirements are around 75 dB. However, 16bit DSPs using single precision computations will not be adequate for precise processing 16bit signals. When using 16bit AD and DA Converters in an audio system that will process `CDquality' signals having a dynamic range of 90  96 dB, a 16bit data path may not be adequate as a result of truncation and rounding errors accumulating during execution of the DSP algorithm. Doubleprecision routines can be utilized to lower the digital filter's noise floor as long as the software overhead is available.
While complexity for new DSP algorithms increase as audio standards and requirements are increasing, designers are looking to 18bit, 20bit, and 24bit converters to increase the signal quality. A 16bit DSP will not be adequate due to these higher resolution converter's dynamic range capabilities exceeding a 16bit DSP processor. However, a 16bit DSP may still be able to interface to these higher precision converters, but this would then require the use of doubleprecision arithmetic. Doubleprecision operations slow down the true performance of the processor while increasing programming complexity. Memory requirements for doubleprecision math are doubled. Even if doubleprecision math can be used, the interfaces to these higher precision converters in many cases would require glue logic to move the data to/from the DSP.
At least 24 bits are required in processing if the quality of 16 bits is to be preserved. However, even with 24bit processing, it has been demonstrated that care would need to be taken to ensure the noise floor of the digital filter algorithm is not greater than the established noise floor of the 16 bit signal, especially for recursive IIR audio filters. Recursive IIR filters can introduce quantization noise above the noise floor of a 16bit converter when using a 24bit DSP [2, 5] and therefore 24bit processing requires software overhead to lower the digital filter's noise floor. Again, double precision math is an option, but this can add overhead by as much as a factor of five.
Using a 32bit, fixedpoint DSP will give additional benefit of ensuring 16bit signal quality is not impaired during arithmetic computations. Thus, the higher resolution of the 32bit DSP will eliminate quantization noise from showing up in the D/A converter output, providing improved SignaltoNoise (SNR) ratio over 16 and 24bit DSPs.
When processing 16bit audio data, the use of 32bit processing is especially useful for complex recursive processing using IIR filters. For example, parametric and graphic equalizer implementations using cascaded 2ndorder IIR filters, and comb/allpass filters for audio are more robust using 32bit math. A 32bit processor operating on 16 or 20bit data removes the filter structure implementation restrictions that are present for 24bit processors. Any filter structure of choice can then be uses without worrying about the level of the noise floor. Doubleprecision and errorfeedback schemes are therefore eliminated. With 16bits below the noise floor on a 32bit DSP, quantization errors would have to accumulate up to 96 dB from the LSB before these errors can be seen by the 16bit D/A converter.
At least 32 bits are required if 24bit signals are to be preserved with complex, mathintensive, or recursive processing. Using 24bit AD and DA converters will require a 32bit DSP in order to offer sufficient precision to ensure that the noise floor of the algorithm will not exceed the 24bit input signal.
The ADSP21161's 32bit capability reduces the implementation burden from the DSP programmer by ensuring that the quantization error from computations does not go above the ADC/DAC noise floor. The ADSP21161's 32bit processing can give an additional 48 dB with 8 extra 'guard' bits in the LSBs compared to a 24bit processor to ensure 16bit signal quality is not impaired during recursive filter computations or multiple processing stages before obtaining the final result for the DAC. The ADSP21161 enables more precise placement of poles/zeros with it's 32bit accuracy using native singleprecision arithmetic.
32bit floatingpoint operations contain 24bit precision, with over 1500 dB dynamic range. The wider dynamic range of floatingpoint computations can virtually eliminate the need for scaling input samples to prevent overflow. The ADSP21161's 40bit floating point operations have as much accuracy as a 32bit fixed point computation with a 32bit mantissa. Dynamic range is equivalent to that of 32bit floatingpoint operations.
8. ADSP21161 SIMD SHARC DSP  The 32bit Processor of Choice for Present and Future Audio DSP
The 16, 20 and even 24bit, fixedpoint digital signal processors in use today in the majority of digital audio products are reaching the point where their performance is no longer sufficient to meet the needs both of established and emerging digital audio markets.
To fully realize the potential of the latest digital audio formats now and into the future requires faster, more flexible DSPs with more accurate and more powerful arithmetic. One such processor is the Analog Devices ADSP21161, capable of both fixed and floatingpoint arithmetic. The ADSP21161 processor contains the ADSP2116x SHARC SIMD core (a SIMD processor uses two identical set of ALU, MAC and Shifter) and its dual computational unit supports the following data types:
 32bit fixedpoint
 32bit IEEE 754/854 floatingpoint
 40bit floatingpoint
"32bit processing is required if 24bit audio signals are to be preserved for complex, computationallyintensive or recursive audio processing. A 32bit DSP like the ADSP21161 offers sufficient precision to ensure that the noise floor of the algorithm will not exceed the 24bit input signal."
The majority of DSP applications in the consumer audio sector currently use 16 or 24bit fixedpoint DSPs for audio processing. However, as the professional and consumer audio market expands in terms of both variety and requirements for high fidelity, these DSP technologies will no longer be adequate to deliver the accuracy and flexibility of DSP processing required. The three data types supported by ADSP21161 make it ideal for satisfying the demand for improved sound quality. In addition, the ADSP21161 includes many other features which make it highly flexible and capable of meeting the needs of developers for a wide variety of applications. These other features include:
 100 MHz provides 200 MIPS, 600 MFLOPS
 1 Megabit of internal memory
 2 link ports for bytewide dedicated interprocessor communication at 100 MHz
 8 bidirectional serial data paths
 I2S support provides 16 programmable direction audio channels, configurable as inputs or outputs
 12 programmable I/O pins for performing 'microcontroller'type' housekeeping tasks
 2 external port and 8 serial port DMA channels
 Glueless Multiprocessing with up to six ADSP21161s in a cluster
 SDRAM interface for bulk storage of lengthy audio delay lines
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Glossary for Some Common A/D and D/A Audio Converter Terms
 Signaltonoise Ratio (SNR or S/N)
This is the ratio of the input signal S to the background noise N in a system. For an ideal AD converter with a sine wave input, the SNR related to the resolution n is SNR(RMS) = 6.02n + 1.76 dB.
Thus, the resolution and quantization level will establish the noise floor. Random system noise will reduce the SNR.
 Quantization Error
All ADs will have at least a minimum error as a result of the discrete or finite specs that represent the analog input, and this error is directly proportional to the resolution.
Quantization Uncertainty Error = +/ .5 LSB
 (Spurious Free) Dynamic Range
This is the ratio of the fullscale input or output signal to the highest harmonic or spurious input/output noise component amplitude. Essentially, this is an indication of how far it is possible to go below the fullscale input signal without hitting noise or distortion. This is usually measured from 0 to 20 kHz and is expressed in decibels (dB). Dynamic range is measured with a 60 dB input signal and is calculated as follows:
Dynamic Range = (S/[THD+N]) + 60 dB
Dynamic Range of a digital signal is defined as the ratio of the maximum full scale signal representation to the smallest signal the DSP or converter can represent. For an Nbit system, the ratio is theoretically equal to 6.02N.
Note: Spurious harmonics are below the noise with a 60 dB input, so the noise level establishes the dynamic range. This is the recommendation of AES and EIAJ.
 Total Harmonic Distortion
A very important specification in audio systems, the THD is defined to be the RMS (rootmeansquare) ratio of the sum of all spectral components (harmonic distortion amplitudes) to the original fullscale input amplitude. It is caused by the AD converter nonlinearities.
 Total Harmonic Distortion + Noise (THD+N)
The ratio of the rootmeansquare value of a fullscale fundamental input signal to the RMS sum of all other spectral components in the passband, expressed in decibels (dB) and percentages.

John Tomarakos
DSP Field Applications