Chapter 1 W hy DSP? In an Instant ● D SP Defi nitions ● T he Need for DSP ● L earning Digital Signal Processing Techniques ● I nstant Summary DSP Defi nitions T he acronym D SP is used for two terms, d igital signal processing and digital sig- nal processor , both of which are covered in this book. D igital signal processing is performing signal processing using digital techniques with the aid of digital hard- ware and/or some kind of computing device. Signal processing can of course be analog as well, but, for a variety of reasons, we may prefer to handle the process- ing digitally. A digital computer or processor that is designed especially for signal processing applications is called a digital signal processor . T HE NEED FOR DSP T o understand the relative merits of analog and digital processing, it is conve- nient to compare the two techniques in a common application. Figure 1.1 shows two approaches to recording sounds such as music or speech. Figure 1.1a is the analog approach. It works like this: ● Sound waves impact the microphone, where they are converted to electrical impulses. ● These electrical signals are amplified, then converted to magnetic fields by the recording head. ● As the magnetic tape moves under the head, the intensity of the magnetic fields is stored on the tape. www.newnespress.com 0022__HH88997766__CChh0011..iinndddd 11 99//44//22000088 11::2288::4466 PPMM 2 Digital Signal Processing: Instant Access Analog signal in Read head Analog signal out Write head Direction of tape travel (a) Analog signal recording. Analog signal out Analog signal in Computer Signal converted Numbers converted to numbers to signal (b) Digital signal recording. FIGURE 1.1 A nalog and digital systems The playback process is just the inverse of the recording process: ● As the magnetic tape moves under the playback head, the magnetic field on the tape is converted to an electrical signal. ● The signal is then amplified and sent to the speaker. The speaker converts the amplified signal back to sound waves. The advantage of the analog process is twofold: first, it is conceptually quite simple. Second, by definition, an analog signal can take on virtually an infinite number of values within the signal’s dynamic range. Unfortunately, this analog process is inherently unstable. The amplifiers are subject to gain variation over temperature, humidity, and time. The magnetic tape stretches and shrinks, thus distorting the recorded signal. The magnetic fields them- selves will, over time, lose some of their strength. Variations in the speed of the motor driving the tape cause additional distortion. All of these factors com- bine to ensure that the output signal will be considerably lower in quality than the input signal Each time the signal is passed on to another analog process, these adverse effects are multiplied. It is rare for an analog system to be able to make more than two or three generations of copies. Now let’s look at the digital process as shown in Figure 1.1b : ● As in the analog case, the sound waves impact the microphone and are con- verted to electrical signals. These electrical signals are then amplified to a usable level. ● The electrical signals are measured or, in other words, they are converted to numbers. ● These numbers can now be stored or manipulated by a computer just as any other numbers are. www.newnespress.com 0022__HH88997766__CChh0011..iinndddd 22 99//44//22000088 11::2288::4477 PPMM Chapter 1 Why DSP? 3 ● To play back the signal, the numbers are simply converted back to electri- cal signals. As in the analog case, these signals are then used to drive a speaker. There are two distinct disadvantages to the digital process: first, it is far more complicated than the analog process; second, computers can only handle numbers of finite resolution. Thus, the (potentially) “ infinite resolution ” of the analog signal is lost. Insider Info T he first major contribution in the area of digital filter synthesis was made by Kaiser at Bell Laboratories. His work showed how to design useful filters using the bilinear transform. Further, in about 1965 the famous paper by Cooley and Turkey was published. In this paper, FFT (fast Fourier transform), an efficient and fast way of performing the DFT (discrete Fourier transform) was demonstrated. A dvantages of DSP Obviously, there must be some compensating benefits of the digital process, and indeed there are. First, once converted to numbers, the signal is uncon- ditionally stable. Using techniques such as error detection and correction, it is possible to store, transmit, and reproduce numbers with no corruption. The twentieth generation of recording is therefore just as accurate as the first generation. Insider Info T he problems with analog signal reproduction have some interesting implica- tions. Future generations will never really know what the Beatles sounded like, for example. The commercial analog technology of the 1960s was simply not able to accurately record and reproduce the signals. Several generations of analog signals were needed to reproduce the sound: First, a master tape would be recorded, and then mixed and edited; from this, a metal master record would be produced, from which would come a plastic impression. Each step of the process was a new gen- eration of recording, and each generation acted on the signal like a filter, reducing the frequency content and skewing the phase. As with the paintings in the Sistine Chapel, the true colors and brilliance of the original art is lost to history. Things are different for today s musicians. A thousand years from now historians will be able to accurately play back the digitally mastered CDs of today. The discs them- selves may well deteriorate, but before they do, the digital numbers on them can be copied with perfect accuracy. Signals stored digitally are really just large arrays of numbers. As such, they are immune to the physical limitations of analog signals. www.newnespress.com 0022__HH88997766__CChh0011..iinndddd 33 99//44//22000088 11::2288::4477 PPMM 4 Digital Signal Processing: Instant Access T here are other significant advantages to processing signals digitally. Geophysicists were one of the first groups to apply the techniques of signal pro- cessing. The seismic signals of interest to them are often of very low frequency, from 0.01 Hz to 10 Hz. It is difficult to build analog filters that work at these low frequencies. Component values must be so large that physically implementing the filter may well be impossible. Once the signals have been converted to digi- tal numbers, however, it is a straightforward process to program a computer to perform the filtering. Other advantages to digital signals abound. For example, DSP can allow large bandwidth signals to be sent over narrow bandwidth channels. A 20-kHz signal can be digitized and then sent over a 5-kHz channel. The signal may take four times as long to get through the narrower bandwidth channel, but when it comes out the other side it can be reconstructed to its full 20-kHz bandwidth. In the same way, communications security can be greatly improved through DSP. Since the signal is sent as numbers, it can be easily encrypted. When received, the numbers are decrypted and then reproduced as the original sig- nal. Modern “ secure telephone ” DSP systems allow this processing to be done with no detectable effect on the conversation. T echnology Trade-offs DSP has several major advantages over analog signal processing techniques, including: ● Essentially perfect reproducibility ● Guaranteed accuracy (no individual tuning and pruning needed) ● Well-suited for volume production LEARNING DIGITAL SIGNAL PROCESSING TECHNIQUES The most important first step of studying any subject is to grasp the overall picture and to understand the basics before diving into the depths. With that in mind, the goal of this book is to provide a broad introduction and overview of DSP techniques and applications. The authors seek to bring an intuitive under- standing of the concepts and systems involved in the field of DSP engineering. O nly a few years ago, DSP techniques were considered advanced and eso- teric subjects, their use limited to research labs or advanced applications such as radar identification. Today, the technology has found its way into virtually every segment of electronics. Computer graphics, mobile entertainment and commu- nication devices, and automobiles are just a few of the common examples. T he rapid acceptance and commercialization of this technology has presented the modern design engineer with a serious challenge: either gain a working knowledge of these techniques or risk obsolescence. Traditionally, engineers have had two options for acquiring new skills: go back to school, or turn to vendors ’ www.newnespress.com 0022__HH88997766__CChh0011..iinndddd 44 99//44//22000088 11::2288::4477 PPMM Chapter 1 Why DSP? 5 technical documentation. In the case of DSP, neither of these is a particularly good option. Undergraduate programs—and even many graduate programs—devoted to DSP are really only thinly disguised courses in the mathematical discipline known as complex analysis. These programs do not aim to teach a working knowledge of DSP, but rather to prepare students for graduate research on DSP topics. Much of the information that is needed to comprehend the “ whys and wherefores ” of DSP are not covered. Manufacturer documentation is often of little more use to the uninitiated. Application notes and design guides usually focus on particular features of the vendor’s instruction set or architecture. I n this book, we hope to bridge the gap between the theory of DSP and the practical knowledge necessary to understand a working DSP system. The math- ematics is not ignored; you will find many sophisticated mathematical relation- ships in thumbing through the pages of this book. What is left out, however, are the formal proofs, the esoteric discussions, and the tedious mathematical exercises. In their place are background discussions explaining how and why the math is important, examples to run on any general-purpose computer, and tips that can help you gain a comfortable understanding of the DSP processes. INSTANT SUMMARY ● Digitally processing a signal allows us to do things with signals that would be difficult, or impossible, with analog approaches. ● With modern components and techniques, these advantages can often be realized economically and efficiently. www.newnespress.com 0022__HH88997766__CChh0011..iinndddd 55 99//44//22000088 11::2288::4488 PPMM Chapter 2 T he Analog-Digital Interface In an Instant ● D efi nitions ● Number Representations ● S ampling and Reconstruction ● Digital-to-Analog Conversion ● Q uantization ● Analog-to-Digital Conversion ● E ncoding and Modulation ● Instant Summary Defi nitions In most systems, whether electronic, financial or social, the majority of prob- lems arise in the interface between different subparts. This is also true for digital signal processing systems. Most signals in real life are continuous in amplitude and time—that is, a nalog —but our digital system is working with amplitude- and time-discrete signals, or so-called d igital signals. So, the input signals entering our system need to be converted from analog to digital form before the actual signal processing can take place. For the same reason, the output signals from our DSP device usually need to be reconverted back from digital to analog form, to be used in, for instance, hydrau- lic valves or loudspeakers or other analog actuators. These conversion processes between the analog and digital world also add some problems to our system. These matters will be addressed in this chapter, together with a brief presentation of some common techniques to perform the actual conversion processes. F irst we will define some of the important terms encountered in this chapter. Sampling is the process of going from a continuous signal to a discrete signal. An analog-to-digital converter (ADC) is a device that converts an analog voltage into a digital number. There are a number of different types, but the most common ones used in DSP are the s uccessive approximation register (SAR) and the flash con- verter . A d igital-to-analog converter converts a digital number to an analog voltage. All of these terms will be further explained as we move through the material in this chapter. www.newnespress.com 0033__HH88997766__CChh0022..iinndddd 77 99//55//22000088 22::4455::3399 PPMM 8 Digital Signal Processing: Instant Access SAMPLING AND RECONSTRUCTION Recall that sampling is how we go from a continuous (analog) signal to a discrete (digital) signal. Sampling can be regarded as multiplying the time- continuous signal g (t ) with a train of unit pulses p ( t ) (see Figure 2.1 ) (cid:4)∞ g#(t)(cid:2)g(t)p(t)(cid:2) ∑ g(nT)δ(t(cid:3)nT) (2.1) n(cid:2)(cid:3)∞ where g# ( t ) is the sampled signal. Since the unit pulses are either one or zero, the multiplication can be regarded as a pure switching operation. The time period T between the unit pulses in the pulse train is called the sampling period . In most cases, this period is constant, resulting in “ equidis- tant sampling. ” In most systems today, it is common to use one or more con- stant sampling periods. The sampling period T is related to the s ampling rate or sampling frequency f such that s ω 1 f (cid:2) s (cid:2) (2.2) s 2π T Insider Info T he sampling period does not have to be constant. In some systems, many differ- ent sampling periods are used (called m ultirate sampling ). In other applications, the sampling period may be a stochastic variable, resulting in r andom sampling , which complicates the analysis considerably. The process of sampling implies reduction of knowledge. For the time- continuous signal, we know the value of the signal at every instant of time, but for the sampled version (the time-discrete signal) we only know the value at specific points in time. If we want to reconstruct the original time-continuous signal from the time-discrete sampled version, we have to make more or less qualified interpolations of the values in between the sampling points. If our interpolated values differ from the true signal, we have introduced distortion in our reconstructed signal. g(t) g#(t) p(t) FIGURE 2.1 S ampling viewed as a multiplication process www.newnespress.com 0033__HH88997766__CChh0022..iinndddd 88 99//55//22000088 22::4455::4400 PPMM Chapter 2 The Analog-Digital Interface 9 If the sampling frequency is less than twice the maximum analog signal frequency, a phenomenon called a liasing will occur, which distorts the sam- pled signal. We will discuss aliasing in more detail in the next chapter. Key Concept In order to avoid aliasing distortion in the sampled signal, it is imperative that the bandwidth of the original time-continuous signal being sampled is smaller than half the sampling frequency (also called the Nyquist frequency). T o avoid aliasing distortion in practical cases, the sampling device is always preceded by some kind of low-pass filter (a ntialiasing filter ) to reduce the bandwidth of the incoming signal. This signal is often quite complicated and may contain a large number of frequency components. Since it is impossible to build perfect filters, there is a risk of too-high-frequency components leaking into the sampler, causing aliasing distortion. We also have to be aware that high- frequency interference may somehow enter the signal path after the low-pass fil- ter, and we may experience aliasing distortion even though the filter is adequate. If the Nyquist criteria is met and hence no aliasing distortion is present, we can reconstruct the original bandwidth-limited, time-continuous signal g ( t ) in an unambiguous way. QUANTIZATION The sampling process described in the previous section is the process of con- verting a continuous-time signal into a discrete-time signal, while q uantization converts a signal continuous in amplitude into a signal discrete in amplitude. Quantization can be thought of as classifying the level of the continuous- valued signal into certain bands. In most cases, these bands are equally spaced over a given range and undesired nonlinear band spacing may cause harmonic distortion. Every band is assigned a code or numerical value. Once we have decided to which band the present signal level belongs, the corresponding code can be used to represent the signal level. Most systems today use the binary code; i.e., the number of quantization intervals N are N (cid:2)2n (2.3) where n is the word length of the binary code. For example, with n (cid:2) 8 bits we get a r esolution of N (cid:2) 256 bands, n (cid:2) 12 yields N (cid:2) 4096, and n (cid:2) 16 gives N (cid:2) 65536 bands. Obviously, the more bands we have—i.e., the longer the word length—the better resolution we obtain. This in turn renders a more accurate representation of the signal. www.newnespress.com 0033__HH88997766__CChh0022..iinndddd 99 99//55//22000088 22::4455::4400 PPMM 10 Digital Signal Processing: Instant Access Insider Info A nother way of looking at resolution of a quantization process is to define the dynamic range as the ratio between the strongest and the weakest signal level that can be represented. The dynamic range is often expressed in decibels. Since every new bit of word length being added increases the number of bands by a factor of 2 the corresponding increase in dynamic range is 6 dB.Hence, an 8-bit system has a dynamic range of 48 dB, a 12-bit system has 72 dB, etc. (This of course only applies for linear band spacing.) ENCODING AND MODULATION A ssuming we have converted our analog signals to numbers in the digital world, there are many ways to e ncode the digital information into the shape of electrical signals. This process is called m odulation . The most common method is probably pulse code modulation (PCM). There are two common ways of transmitting PCM, and they are p arallel and serial mode. In an example of the parallel case, the information is encoded as voltage levels on a number of wires, called a parallel bus. We are using binary signals, which means that only two voltage levels are used, (cid:4) 5 V corresponding to a binary “ 1 ” (or “ true ” ), and 0 V meaning a binary “ 0 ” (or “ false ” ). Hence, every wire carrying 0 or (cid:4) 5 V contributes a binary digit ( “ bit ” ). A parallel bus consisting of eight wires will therefore carry 8 bits, a byte consisting of bits D0, D1–D7 ( Figure 2.2 ). T echnology Trade-offs Parallel buses are able to transfer high information data rates, since an entire data word (a sampled value) is being transferred at a time. This transmission can take place between, for instance, an analog-to-digital converter (ADC) and a digital signal processor (DSP). One drawback with parallel buses is that they D0 0 (1) D1 1 (2) D2 1 (4) D0 D1 D2 D3 D4 D5 D6 D7 D3 0 (8) D4 1 (16) 0 1 1 0 1 0 0 1 D5 0 (32) D6 0 (64) D7 1 (128) FIGURE 2.2 Example, a byte (96H) encoded (weights in parenthesis) using PCM in parallel mode (parallel bus, 8 bits, eight wires) and in serial mode as an 8-bit pulse train (over one wire) www.newnespress.com 0033__HH88997766__CChh0022..iinndddd 1100 99//55//22000088 22::4455::4411 PPMM