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CHAPTER 13 The Digital Processor
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The same block diagram notation can, of course, be extended to any number of cascaded or paralleled stages. Problem 312 Write the equation H z in the form of eq. (606). Problem 313 The individual unit pulse responses of three DT processors are as follows: z z z H1 z H2 z H3 z 2 z 0:2 z 0:4 z 0:8z 0:15 If the three processors are connected as in the block diagram below, nd the unit pulse response H z for the entire connection. Write nal answer in form of eq. (606). 2z3 4z2 z z3 5z2 6z 9
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Problem 314 Repeat problem 313 if the same three processors are connected in the con guration shown to the right. Problem 315 Suppose a single unit pulse of voltage p nT is applied to the input of the processor of problem 313. Find the output of the network 3T seconds later. (Answer: 1.25 volts) Problem 316 Sketch the block diagram of the Direct Form II processor (Fig. 356) having the transfer function H z 2z3 1:3z2 0:9z z3 2:2z2 1:5z 0:75
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CHAPTER 13 The Digital Processor
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Problem 317 Determine whether the following Direct Form II processor is stable or unstable.
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Problem 318 Determine whether the Direct Form II processor to the right is stable or unstable.
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Digital Filters; The Basic Algebra
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Signals can be, and are, studied in both the time domain and the frequency domain. In the time domain we principally study the manner in which the amplitude and time delay of a signal change with time. In the frequency domain we study the amplitudes and phase shifts of the di erent sinusoidal frequency components present in a signal (the fundamental and harmonics, as outlined in note 18 in the Appendix). The result of such a study is summarized in terms of the frequency response characteristic of a system. An electric FILTER is a network designed to have a SPECIFIC FORM of frequency response characteristic. Thus we have low-pass lters, high-pass lters, and so on. You ll recall that it s convenient to display such results graphically, in the form of frequency response curves. By frequency it s always understood that we mean the frequencies of the sinusoidal component waves of a signal. As always, frequency in radians per second is denoted by omega, !, while frequency in cycles per second (hertz) is denoted by f , in which, as you know, ! 2f . In practical work it s convenient to express results in terms of FREQUENCY of SINUSOIDAL waves of voltage and current. Thus in the time domain we work with the basic equations v sin !t and v cos !t. We have found, however, that the ALGEBRAIC work can be greatly simpli ed if we are not restricted to the use of real numbers only but are allowed to work in the total complex plane of all numbers. This is because the algebraic operations of multiplication, division, roots, and powers are easier to express and carry out in the complex plane than in
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CHAPTER 13 The Digital Processor
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