Real-Time Digital Signal Processing - Chapter 1: Introduction to Real-Time Digital Signal Processing

Introduction to Real-Time Digital Signal Processing Signals can be divided into three categories ± continuous-time analog signals,discrete-time signals, and digital signals.. These signa

Introduction to Real-Time

Digital Signal Processing

Signals can be divided into three categories ± continuous-time (analog) signals,discrete-time signals, and digital signals The signals that we encounter daily are mostlyanalog signals These signals are defined continuously in time, have an infinite range

of amplitude values, and can be processed using electrical devices containing bothactive and passive circuit elements Discrete-time signals are defined only at a particularset of time instances Therefore they can be represented as a sequence of numbers thathave a continuous range of values On the other hand, digital signals have discretevalues in both time and amplitude In this book, we design and implement digitalsystems for processing digital signals using digital hardware However, the analysis

of such signals and systems usually uses discrete-time signals and systems for ematical convenience Therefore we use the term `discrete-time' and `digital' inter-changeably

math-Digital signal processing (DSP) is concerned with the digital representation of signalsand the use of digital hardware to analyze, modify, or extract information from thesesignals The rapid advancement in digital technology in recent years has created theimplementation of sophisticated DSP algorithms that make real-time tasks feasible Agreat deal of research has been conducted to develop DSP algorithms and applications.DSP is now used not only in areas where analog methods were used previously, but also

in areas where applying analog techniques is difficult or impossible

There are many advantages in using digital techniques for signal processing ratherthan traditional analog devices (such as amplifiers, modulators, and filters) Some of theadvantages of a DSP system over analog circuitry are summarized as follows:

1 Flexibility Functions of a DSP system can be easily modified and upgraded withsoftware that has implemented the specific algorithm for using the same hardware.One can design a DSP system that can be programmed to perform a wide variety oftasks by executing different software modules For example, a digital camera may

be easily updated (reprogrammed) from using JPEG ( joint photographic expertsgroup) image processing to a higher quality JPEG2000 image without actuallychanging the hardware In an analog system, however, the whole circuit designwould need to be changed

Real-Time Digital Signal Processing Sen M Kuo, Bob H Lee

Copyright # 2001 John Wiley & Sons Ltd ISBNs: 0-470-84137-0 (Hardback); 0-470-84534-1 (Electronic)

2 Reproducibility The performance of a DSP system can be repeated precisely fromone unit to another This is because the signal processing of DSP systems workdirectly with binary sequences Analog circuits will not perform as well from eachcircuit, even if they are built following identical specifications, due to componenttolerances in analog components In addition, by using DSP techniques, a digitalsignal can be transferred or reproduced many times without degrading its signalquality.

3 Reliability The memory and logic of DSP hardware does not deteriorate withage Therefore the field performance of DSP systems will not drift with changingenvironmental conditions or aged electronic components as their analog counter-parts do However, the data size (wordlength) determines the accuracy of a DSPsystem Thus the system performance might be different from the theoretical expect-ation

4 Complexity Using DSP allows sophisticated applications such as speech or imagerecognition to be implemented for lightweight and low power portable devices This

is impractical using traditional analog techniques Furthermore, there are someimportant signal processing algorithms that rely on DSP, such as error correctingcodes, data transmission and storage, data compression, perfect linear phase filters,etc., which can barely be performed by analog systems

With the rapid evolution in semiconductor technology in the past several years, DSPsystems have a lower overall cost compared to analog systems DSP algorithms can bedeveloped, analyzed, and simulated using high-level language and software tools such asC=C‡‡ and MATLAB (matrix laboratory) The performance of the algorithms can beverified using a low-cost general-purpose computer such as a personal computer (PC).Therefore a DSP system is relatively easy to develop, analyze, simulate, and test.There are limitations, however For example, the bandwidth of a DSP system islimited by the sampling rate and hardware peripherals The initial design cost of aDSP system may be expensive, especially when large bandwidth signals are involved.For real-time applications, DSP algorithms are implemented using a fixed number ofbits, which results in a limited dynamic range and produces quantization and arithmeticerrors

1.1 Basic Elements of Real-Time DSP Systems

There are two types of DSP applications ± non-real-time and real time Non-real-timesignal processing involves manipulating signals that have already been collected anddigitized This may or may not represent a current action and the need for the result

is not a function of real time Real-time signal processing places stringent demands

on DSP hardware and software design to complete predefined tasks within a certaintime frame This chapter reviews the fundamental functional blocks of real-time DSPsystems

The basic functional blocks of DSP systems are illustrated in Figure 1.1, where a world analog signal is converted to a digital signal, processed by DSP hardware in

real-Other digital systems

Anti-aliasing

x(n)

DSP hardware

Other digital systems DAC

Reconstruction

x(t) x⬘(t)

Figure 1.1 Basic functional blocks of real-time DSP system

digital form, and converted back into an analog signal Each of the functional blocks inFigure 1.1 will be introduced in the subsequent sections For some real-time applica-tions, the input data may already be in digital form and/or the output data may not need

to be converted to an analog signal For example, the processed digital information may

be stored in computer memory for later use, or it may be displayed graphically In otherapplications, the DSP system may be required to generate signals digitally, such asspeech synthesis used for cellular phones or pseudo-random number generators forCDMA (code division multiple access) systems

1.2 Input and Output Channels

In this book, a time-domain signal is denoted with a lowercase letter For example, x…t†

in Figure 1.1 is used to name an analog signal of x with a relationship to time t The timevariable t takes on a continuum of values between 1 and 1 For this reason we say

x…t† is a continuous-time signal In this section, we first discuss how to convert analogsignals into digital signals so that they can be processed using DSP hardware Theprocess of changing an analog signal to a xdigital signal is called analog-to-digital (A/D)conversion An A/D converter (ADC) is usually used to perform the signal conversion.Once the input digital signal has been processed by the DSP device, the result, y…n†, isstill in digital form, as shown in Figure 1.1 In many DSP applications, we need toreconstruct the analog signal after the digital processing stage In other words, we mustconvert the digital signal y…n† back to the analog signal y…t† before it is passed to anappropriate device This process is called the digital-to-analog (D/A) conversion, typi-cally performed by a D/A converter (DAC) One example would be CD (compact disk)players, for which the music is in a digital form The CD players reconstruct the analogwaveform that we listen to Because of the complexity of sampling and synchronizationprocesses, the cost of an ADC is usually considerably higher than that of a DAC.1.2.1 Input Signal Conditioning

As shown in Figure 1.1, the analog signal, x0…t†, is picked up by an appropriateelectronic sensor that converts pressure, temperature, or sound into electrical signals

INPUT AND OUTPUT CHANNELS 3

For example, a microphone can be used to pick up sound signals The sensor output,

x0…t†, is amplified by an amplifier with gain value g The amplified signal is

The gain value g is determined such that x…t† has a dynamic range that matches theADC For example, if the peak-to-peak range of the ADC is 5 volts (V), then g may beset so that the amplitude of signal x…t† to the ADC is scaled between  5V In practice, it

is very difficult to set an appropriate fixed gain because the level of x0…t† may beunknown and changing with time, especially for signals with a larger dynamic rangesuch as speech Therefore an automatic gain controller (AGC) with time-varying gaindetermined by DSP hardware can be used to effectively solve this problem

of two functional blocks ± an ideal sampler (sample and hold) and a quantizer ing an encoder) Analog-to-digital conversion carries out the following steps:

(includ-1 The bandlimited signal x…t† is sampled at uniformly spaced instants of time, nT,where n is a positive integer, and T is the sampling period in seconds This samplingprocess converts an analog signal into a discrete-time signal, x…nT†, with continuousamplitude value

2 The amplitude of each discrete-time sample is quantized into one of the 2B levels,where B is the number of bits the ADC has to represent for each sample Thediscrete amplitude levels are represented (or encoded) into distinct binary words

x…n† with a fixed wordlength B This binary sequence, x…n†, is the digital signal forDSP hardware

The reason for making this distinction is that each process introduces different tions The sampling process brings in aliasing or folding distortions, while the encodingprocess results in quantization noise.

in Figure 1.3 The signal x…nT† is an impulse train with values equal to the amplitude

of x…t† at time nT The analog input signal x…t† is continuous in both time andamplitude The sampled signal x…nT† is continuous in amplitude, but it is definedonly at discrete points in time Thus the signal is zero except at the sampling instants

t ˆ nT

In order to represent an analog signal x…t† by a discrete-time signal x…nT† accurately,two conditions must be met:

1 The analog signal, x…t†, must be bandlimited by the bandwidth of the signal fM

2 The sampling frequency, fs, must be at least twice the maximum frequency ponent fM in the analog signal x…t† That is,

This is Shannon's sampling theorem It states that when the sampling frequency isgreater than twice the highest frequency component contained in the analog signal, theoriginal signal x…t† can be perfectly reconstructed from the discrete-time sample x…nT†.The sampling theorem provides a basis for relating a continuous-time signal x…t† with

Time, t x(nT)

x(t)

Figure 1.3 Example of analog signal x…t† and discrete-time signal x…nT†

INPUT AND OUTPUT CHANNELS 5

the discrete-time signal x…nT† obtained from the values of x…t† taken T seconds apart Italso provides the underlying theory for relating operations performed on the sequence

to equivalent operations on the signal x…t† directly

The minimum sampling frequency fsˆ 2fM is the Nyquist rate, while fN ˆ fs=2 isthe Nyquist frequency (or folding frequency) The frequency interval ‰ fs=2, fs=2Š

is called the Nyquist interval When an analog signal is sampled at sampling frequency,

fs, frequency components higher than fs=2 fold back into the frequency range ‰0, fs=2Š.This undesired effect is known as aliasing That is, when a signal is sampledperversely to the sampling theorem, image frequencies are folded back into the desiredfrequency band Therefore the original analog signal cannot be recovered from thesampled data This undesired distortion could be clearly explained in the frequencydomain, which will be discussed in Chapter 4 Another potential degradation is due totiming jitters on the sampling pulses for the ADC This can be negligible if a higherprecision clock is used

For most practical applications, the incoming analog signal x…t† may not be limited Thus the signal has significant energies outside the highest frequency ofinterest, and may contain noise with a wide bandwidth In other cases, the samplingrate may be pre-determined for a given application For example, most voice commu-nication systems use an 8 kHz (kilohertz) sampling rate Unfortunately, the maximumfrequency component in a speech signal is much higher than 4 kHz Out-of-band signalcomponents at the input of an ADC can become in-band signals after conversionbecause of the folding over of the spectrum of signals and distortions in the discretedomain To guarantee that the sampling theorem defined in Equation (1.2.3) can befulfilled, an anti-aliasing filter is used to band-limit the input signal The anti-aliasingfilter is an analog lowpass filter with the cut-off frequency of

band-fcfs

Ideally, an anti-aliasing filter should remove all frequency components above theNyquist frequency In many practical systems, a bandpass filter is preferred in order

to prevent undesired DC offset, 60 Hz hum, or other low frequency noises For example,

a bandpass filter with passband from 300 Hz to 3200 Hz is used in most tion systems

telecommunica-Since anti-aliasing filters used in real applications are not ideal filters, they cannotcompletely remove all frequency components outside the Nyquist interval Any fre-quency components and noises beyond half of the sampling rate will alias into thedesired band In addition, since the phase response of the filter may not be linear, thecomponents of the desired signal will be shifted in phase by amounts not proportional totheir frequencies In general, the steeper the roll-off, the worse the phase distortionintroduced by a filter To accommodate practical specifications for anti-aliasing filters,the sampling rate must be higher than the minimum Nyquist rate This technique isknown as oversampling When a higher sampling rate is used, a simple low-cost anti-aliasing filter with minimum phase distortion can be used

Example 1.1: Given a sampling rate for a specific application, the sampling periodcan be determined by (1.2.2)

(a) In narrowband telecommunication systems, the sampling rate fsˆ 8 kHz,thus the sampling period T ˆ 1=8 000 seconds ˆ 125 ms (microseconds).Note that 1 ms ˆ 10 6seconds.

(b) In wideband telecommunication systems, the sampling is given as

1.2.4 Quantizing and Encoding

In the previous sections, we assumed that the sample values x…nT† are representedexactly with infinite precision An obvious constraint of physically realizable digitalsystems is that sample values can only be represented by a finite number of bits.The fundamental distinction between discrete-time signal processing and DSP is thewordlength The former assumes that discrete-time signal values x…nT† have infinitewordlength, while the latter assumes that digital signal values x…n† only have a limitedB-bit

We now discuss a method of representing the sampled discrete-time signal x…nT† as abinary number that can be processed with DSP hardware This is the quantizing andencoding process As shown in Figure 1.3, the discrete-time signal x…nT† has an analogamplitude (infinite precision) at time t ˆ nT To process or store this signal with DSPhardware, the discrete-time signal must be quantized to a digital signal x…n† with a finitenumber of bits If the wordlength of an ADC is B bits, there are 2B different values(levels) that can be used to represent a sample The entire continuous amplitude range isdivided into 2B subranges Amplitudes of waveform that are in the same subrange areassigned the same amplitude values Therefore quantization is a process that represents

an analog-valued sample x…nT† with its nearest level that corresponds to the digitalsignal x…n† The discrete-time signal x…nT† is a sequence of real numbers using infinitebits, while the digital signal x…n† represents each sample value by a finite number of bitswhich can be stored and processed using DSP hardware

The quantization process introduces errors that cannot be removed For example, wecan use two bits to define four equally spaced levels (00, 01, 10, and 11) to classify thesignal into the four subranges as illustrated in Figure 1.4 In this figure, the symbol `o'represents the discrete-time signal x…nT†, and the symbol `' represents the digital signal

x…n†

In Figure 1.4, the difference between the quantized number and the original value isdefined as the quantization error, which appears as noise in the output It is also calledquantization noise The quantization noise is assumed to be random variables that areuniformly distributed in the intervals of quantization levels If a B-bit quantizer is used,the signal-to-quantization-noise ratio (SNR) is approximated by (will be derived inChapter 3)

INPUT AND OUTPUT CHANNELS 7

T 2T 3T

00 01 10 11 Quantization level

Time, t x(t)

of bits in the ADC However, Equation (1.2.5) provides a simple guideline for ing the required bits for a given application For each additional bit, a digital signal hasabout a 6-dB gain in SNR For example, a 16-bit ADC provides about 96 dB SNR Themore bits used to represent a waveform sample, the smaller the quantization noise will

determin-be If we had an input signal that varied between 0 and 5 V, using a 12-bit ADC, whichhas 4096 …212† levels, the least significant bit (LSB) would correspond to 1.22 mVresolution An 8-bit ADC with 256 levels can only provide up to 19.5 mV resolution.Obviously with more quantization levels, one can represent the analog signal moreaccurately The problems of quantization and their solutions will be further discussed inChapter 3

If the uniform quantization scheme shown in Figure 1.4 can adequately representloud sounds, most of the softer sounds may be pushed into the same small value Thismeans soft sounds may not be distinguishable To solve this problem, a quantizer whosequantization step size varies according to the signal amplitude can be used In practice,the non-uniform quantizer uses a uniform step size, but the input signal is compressedfirst The overall effect is identical to the non-uniform quantization For example, thelogarithm-scaled input signal, rather than the input signal itself, will be quantized Afterprocessing, the signal is reconstructed at the output by expanding it The process ofcompression and expansion is called companding (compressing and expanding) Forexample, the m-law (used in North America and parts of Northeast Asia) and A-law(used in Europe and most of the rest of the world) companding schemes are used in mostdigital communications

As shown in Figure 1.1, the input signal to DSP hardware may be a digital signalfrom other DSP systems In this case, the sampling rate of digital signals from otherdigital systems must be known The signal processing techniques called interpolation ordecimation can be used to increase or decrease the existing digital signals' samplingrates Sampling rate changes are useful in many applications such as interconnectingDSP systems operating at different rates A multirate DSP system uses more than onesampling frequency to perform its tasks

1.2.5 D/A Conversion

Most commercial DACs are zero-order-hold, which means they convert the binaryinput to the analog level and then simply hold that value for T seconds until the nextsampling instant Therefore the DAC produces a staircase shape analog waveform y0…t†,which is shown as a solid line in Figure 1.5 The reconstruction (anti-imaging andsmoothing) filter shown in Figure 1.1 smoothes the staircase-like output signal gener-ated by the DAC This analog lowpass filter may be the same as the anti-aliasing filterwith cut-off frequency fc fs=2, which has the effect of rounding off the corners of thestaircase signal and making it smoother, which is shown as a dotted line in Figure 1.5.High quality DSP applications, such as professional digital audio, require the use ofreconstruction filters with very stringent specifications

From the frequency-domain viewpoint (will be presented in Chapter 4), the output ofthe DAC contains unwanted high frequency or image components centered at multiples

of the sampling frequency Depending on the application, these high-frequency ents may cause undesired side effects Take an audio CD player for example Althoughthe image frequencies may not be audible, they could overload the amplifier and causeinter-modulation with the desired baseband frequency components The result is anunacceptable degradation in audio signal quality

compon-The ideal reconstruction filter has a flat magnitude response and linear phase in thepassband extending from the DC to its cut-off frequency and infinite attenuation inthe stopband The roll-off requirements of the reconstruction filter are similar to those

of the anti-aliasing filter In practice, switched capacitor filters are preferred because oftheir programmable cut-off frequency and physical compactness

1.2.6 Input/Output Devices

There are two basic ways of connecting A/D and D/A converters to DSP devices: serialand parallel A parallel converter receives or transmits all the B bits in one pass, whilethe serial converters receive or transmit B bits in a serial data stream Converters withparallel input and output ports must be attached to the DSP's address and data buses,

y ⬘(t)

Time, t

0 T 2T 3T 4T 5T

Smoothed output signal

Figure 1.5 Staircase waveform generated by a DAC

INPUT AND OUTPUT CHANNELS 9

which are also attached to many different types of devices With different memorydevices (RAM, EPROM, EEPROM, or flash memory) at different speeds hanging onDSP's data bus, driving the bus may become a problem Serial converters can beconnected directly to the built-in serial ports of DSP devices This is why many practicalDSP systems use serial ADCs and DACs.

Many applications use a single-chip device called an analog interface chip (AIC) orcoder/decoder (CODEC), which integrates an anti-aliasing filter, an ADC, a DAC, and areconstruction filter all on a single piece of silicon Typical applications include modems,speech systems, and industrial controllers Many standards that specify the nature of theCODEC have evolved for the purposes of switching and transmission These devicesusually use a logarithmic quantizer, i.e., A-law or m-law, which must be converted into alinear format for processing The availability of inexpensive companded CODEC justi-fies their use as front-end devices for DSP systems DSP chips implement this formatconversion in hardware or in software by using a table lookup or calculation

The most popular commercially available ADCs are successive approximation, dualslope, flash, and sigma-delta The successive-approximation ADC produces a B-bitoutput in B cycles of its clock by comparing the input waveform with the output of adigital-to-analog converter This device uses a successive-approximation register to splitthe voltage range in half in order to determine where the input signal lies According tothe comparator result, one bit will be set or reset each time This process proceedsfrom the most significant bit (MSB) to the LSB The successive-approximation type ofADC is generally accurate and fast at a relatively low cost However, its ability to followchanges in the input signal is limited by its internal clock rate, so that it may be slow torespond to sudden changes in the input signal

The dual-slope ADC uses an integrator connected to the input voltage and a referencevoltage The integrator starts at zero condition, and it is charged for a limited time Theintegrator is then switched to a known negative reference voltage and charged in theopposite direction until it reaches zero volts again At the same time, a digital counterstarts to record the clock cycles The number of counts required for the integratoroutput voltage to get back to zero is directly proportional to the input voltage Thistechnique is very precise and can produce ADCs with high resolution Since theintegrator is used for input and reference voltages, any small variations in temperatureand aging of components have little or no effect on these types of converters However,they are very slow and generally cost more than successive-approximation ADCs

A voltage divider made by resistors is used to set reference voltages at the flash ADCinputs The major advantage of a flash ADC is its speed of conversion, which is simplythe propagation delay time of the comparators Unfortunately, a B-bit ADC needs

…2B 1† comparators and laser-trimmed resistors Therefore commercially availableflash ADCs usually have lower bits

The block diagram of a sigma±delta ADC is illustrated in Figure 1.6 Sigma±deltaADCs use a 1-bit quantizer with a very high sampling rate Thus the requirements for ananti-aliasing filter are significantly relaxed (i.e., the lower roll-off rate and smaller flatresponse in passband) In the process of quantization, the resulting noise power is spreadevenly over the entire spectrum As a result, the noise power within the band of interest islower In order to match the output frequency with the system and increase its resolution,

a decimator is used The advantages of the sigma±delta ADCs are high resolution andgood noise characteristics at a competitive price because they use digital filters

input

− Σ

1-bit DAC

1-bit ADC

1.3.1 DSP Hardware Options

As shown in Figure 1.1, the processing of the digital signal x…n† is carried out using theDSP hardware Although it is possible to implement DSP algorithms on any digitalcomputer, the throughput (processing rate) determines the optimum hardware plat-form Four DSP hardware platforms are widely used for DSP applications:

1 general-purpose microprocessors and microcontrollers …mP†,

2 general-purpose digital signal processors (DSP chips),

3 digital building blocks (DBB) such as multiplier, adder, program controller, and

4 special-purpose (custom) devices such as application specific integrated circuits(ASIC)

The hardware characteristics are summarized in Table 1.1

ASIC devices are usually designed for specific tasks that require a lot of DSP MIPS(million instructions per second), such as fast Fourier transform (FFT) devices andReed±Solomon coders used by digital subscriber loop (xDSL) modems These devicesare able to perform their limited functions much faster than general-purpose DSP chipsbecause of their dedicated architecture These application-specific products enable theuse of high-speed functions optimized in hardware, but they lack the programmability

to modify the algorithm, so they are suitable for implementing defined and tested DSP algorithms Therefore applications demanding high speeds typically employASICs, which allow critical DSP functions to be implemented in the hardware Theavailability of core modules for common DSP functions has simplified the ASIC designtasks, but the cost of prototyping an ASIC device, a longer design cycle, insufficient

Table 1.1 Summary of DSP hardware implementations

Development cost high medium low low

Production cost low high low±medium low±medium

there is no intrinsic difference between the instructions and the data, and that theinstructions can be partitioned into two major fields containing the operation commandand the address of the operand Figure 1.7(b) shows the memory architecture of the vonNeumann model Most general-purpose microprocessors use the von Neumann archi-tecture Operations such as add, move, and subtract are easy to perform However,complex instructions such as multiplication and division are slow since they need aseries of shift, addition, or subtraction operations These devices do not have thearchitecture or the on-chip facilities required for efficient DSP operations They may

be used when a small amount of signal processing work is required in a much largersystem Their real-time DSP performance does not compare well with even the cheapergeneral-purpose DSP devices, and they would not be a cost-effective solution for manyDSP tasks

A DSP chip (digital signal processor) is basically a microprocessor whose architecture

is optimized for processing specific operations at high rates DSP chips with tures and instruction sets specifically designed for DSP applications have been launched

architec-by Texas Instruments, Motorola, Lucent Technologies, Analog Devices, and manyother companies The rapid growth and the exploitation of DSP semiconductor tech-nology are not a surprise, considering the commercial advantages in terms of the fast,flexible, and potentially low-cost design capabilities offered by these devices General-purpose-programmable DSP chip developments are supported by software develop-ment tools such as C compilers, assemblers, optimizers, linkers, debuggers, simulators,and emulators Texas Instruments' TMS320C55x, a programmable, high efficiency, andultra low-power DSP chip, will be discussed in the next chapter

1.3.2 Fixed- and Floating-Point Devices

A basic distinction between DSP chips is their fixed-point or floating-point architectures.The fixed-point representation of signals and arithmetic will be discussed in Chapter 3.Fixed-point processors are either 16-bit or 24-bit devices, while floating-point processorsare usually 32-bit devices A typical 16-bit fixed-point processor, such as theTMS320C55x, stores numbers in a 16-bit integer format Although coefficients andsignals are only stored with 16-bit precision, intermediate values (products) may be kept

at 32-bit precision within the internal accumulators in order to reduce cumulative ing errors Fixed-point DSP devices are usually cheaper and faster than their floating-point counterparts because they use less silicon and have fewer external pins

round-A typical 32-bit floating-point DSP device, such as the TMS320C3x, stores a 24-bitmantissa and an 8-bit exponent A 32-bit floating-point format gives a large dynamicrange However, the resolution is still only 24 bits Dynamic range limitations may bevirtually ignored in a design using floating-point DSP chips This is in contrast to fixed-point designs, where the designer has to apply scaling factors to prevent arithmeticoverflow, which is a very difficult and time-consuming process

Floating-point devices may be needed in applications where coefficients vary in time,signals and coefficients have a large dynamic range, or where large memory structuresare required, such as in image processing Other cases where floating-point devices can

be justified are where development costs are high and production volumes are low Thefaster development cycle for a floating-point device may easily outweigh the extra cost

of the DSP device itself Floating-point DSP chips also allow the efficient use ofthe high-level C compilers and reduce the need to identify the system's dynamic range.1.3.3 Real-Time Constraints

A limitation of DSP systems for real-time applications is that the bandwidth of thesystem is limited by the sampling rate The processing speed determines the rate atwhich the analog signal can be sampled For example, a real-time DSP system demandsthat the signal processing time, tp, must be less than the sampling period, T, in order tocomplete the processing task before the new sample comes in That is,

1.4 DSP System Design

A generalized DSP system design is illustrated in Figure 1.8 For a given application, thetheoretical aspects of DSP system specifications such as system requirements, signalanalysis, resource analysis, and configuration analysis are first performed to define thesystem requirements

1.4.1 Algorithm Development

The algorithm for a given application is initially described using difference equations orsignal-flow block diagrams with symbolic names for the inputs and outputs In docu-menting the algorithm, it is sometimes helpful to further clarify which inputs andoutputs are involved by means of a data flow diagram The next stage of the develop-ment process is to provide more details on the sequence of operations that must beperformed in order to derive the output from the input There are two methods forcharacterizing the sequence of steps in a program: flowcharts or structured descriptions

H A R D W A R E

S O F T W A R E

System requirements specifications

Algorithm development and simulation

Select DSP devices

System integration and debug

System testing and release

Application

Software architecture

Coding and Debugging

Hardware Schematic

Hardware Prototype

Figure 1.8 Simplified DSP system design flow

MATLAB or C/C++

ADC

Other computers

Other computers DAC

Signal generators

DSP algorithms

DSP software Data

files

Data files

Figure 1.9 DSP software development using a general-purpose computer

At the algorithm development stage, we most likely work with high-level DSP tools(such as MATLAB or C=C‡‡) that enable algorithmic-level system simulations Wethen migrate the algorithm to software, hardware, or both, depending on our specificneeds A DSP application or algorithm can be first simulated using a general-purposecomputer, such as a PC, so that it can be analyzed and tested off-line using simulatedinput data A block diagram of general-purpose computer implementation is illustrated

in Figure 1.9 The test signals may be internally generated by signal generators ordigitized from an experimental setup based on the given application The program usesthe stored signal samples in data file(s) as input(s) to produce output signals that will besaved in data file(s)

Advantages of developing DSP software on a general-purpose computer are:

1 Using the high-level languages such as MATLAB, C=C‡‡, or other DSP softwarepackages can significantly save algorithm and software development time In add-ition, C programs are portable to different DSP hardware platforms

2 It is easy to debug and modify programs

3 Input/output operations based on disk files are simple to implement and the iors of the system are easy to analyze

behav-4 Using the floating-point data format can achieve higher precision

5 With point simulation, bit-true verification of an algorithm against point DSP implementation can easily be compared

fixed-1.4.2 Selection of DSP Chips

A choice of DSP chip from many available devices requires a full understanding of theprocessing requirements of the DSP system under design The objective is to select thedevice that meets the project's time-scales and provides the most cost-effective solution.Some decisions can be made at an early stage based on computational power, resolu-tion, cost, etc In real-time DSP, the efficient flow of data into and out of the processor

is also critical However, these criteria will probably still leave a number of candidatedevices for further analysis For high-volume applications, the cheapest device that can

do the job should be chosen For low- to medium-volume applications, there will be atrade-off between development time, development tool cost, and the cost of the DSPdevice itself The likelihood of having higher-performance devices with upwards-compatible software in the future is also an important factor

When processing speed is at a premium, the only valid comparison between devices is

on an algorithm-implementation basis Optimum code must be written for both devicesand then the execution time must be compared Other important factors are memory sizeand peripheral devices, such as serial and parallel interfaces, which are available on-chip

In addition, a full set of development tools and supports are important for DSP chipselection, including:

1 Software development tools, such as assemblers, linkers, simulators, and C pilers

com-2 Commercially available DSP boards for software development and testing beforethe target DSP hardware is available

3 Hardware testing tools, such as in-circuit emulators and logic analyzers

4 Development assistance, such as application notes, application libraries, databooks, real-time debugging hardware, low-cost prototyping, etc

1.4.3 Software Development

The four common measures of good DSP software are reliability, maintainability,extensibility, and efficiency A reliable program is one that seldom (or never) fails.Since most programs will occasionally fail, a maintainable program is one that is easy

to fix A truly maintainable program is one that can be fixed by someone other thanthe original programmer In order for a program to be truly maintainable, it must beportable on more than one type of hardware An extensible program is one that can

be easily modified when the requirements change, new functions need to be added, ornew hardware features need to be exploited An efficient DSP program will use theprocessing capabilities of the target hardware to minimize execution time

A program is usually tested in a finite number of ways much smaller than the number

of input data conditions This means that a program can be considered reliable onlyafter years of bug-free use in many different environments A good DSP program oftencontains many small functions with only one purpose, which can be easily reused byother programs for different purposes Programming tricks should be avoided at allcosts as they will often not be reliable and will almost always be difficult for someoneelse to understand even with lots of comments In addition, use variable names that aremeaningful in the context of the program

As shown in Figure 1.8, the hardware and software design can be conducted at thesame time for a given DSP application Since there is a lot of interdependence factorsbetween hardware and software, the ideal DSP designer will be a true `system' engineer,capable of understanding issues with both hardware and software The cost of hardwarehas gone down dramatically in recent years The majority of the cost of a DSP solutionnow resides in software development This section discussed some issues regardingsoftware development

The software life cycle involves the completion of a software project: the projectdefinition, the detailed specification, coding and modular testing, integration, andmaintenance Software maintenance is a significant part of the cost of a softwaresystem Maintenance includes enhancing the software, fixing errors identified as thesoftware is used, and modifying the software to work with new hardware and software

It is essential to document programs thoroughly with titles and comment statementsbecause this greatly simplifies the task of software maintenance

As discussed earlier, good programming technique plays an essential part in ful DSP application A structured and well-documented approach to programmingshould be initiated from the beginning It is important to develop an overall specifica-tion for signal processing tasks prior to writing any program The specification includesthe basic algorithm/task description, memory requirements, constraints on the programsize, execution time, etc Specification review is an important component of the softwaredevelopment process A thoroughly reviewed specification can catch mistakes beforecode is written and reduce potential code rework risk at system integration stage Thepotential use of subroutines for repetitive processes should also be noted A flowdiagram will be a very helpful design tool to adopt at this stage Program and datablocks should be allocated to specific tasks that optimize data access time and address-ing functions

success-A software simulator or a hardware platform can be used for testing DSP code.Software simulators run on a host computer to mimic the behavior of a DSP chip The