Signal Processing and Linear Systems-B.P.Lathi copy

For systems with memory also known as dynamic systems

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Unformatted text preview: h old, t he signals are functions of space a nd time; such a system is a d istributed-parameter system. 6. S ystems w hose inputs a nd o utputs a re continuous-time signals are continuoustime systems; systems whose inputs and o utputs are discrete-time signals are discrete-time systems. I f a continuous-time signal is sampled, t he resulting signal is a d iscrete-time signal. We can process a continuous-time signal by processing t he samples of this signal with a discrete-time system. 7. S ystems w hose inputs a nd o utputs a re analog signals are analog systems; those whose i nputs a nd o utputs are digital signals are digital systems. 8. I f we c an o btain t he i nput / (t) back from t he o utput y (t) of a system S by some o peration, t he system S is s aid to be invertible. Otherwise t he system is n oninvertible. T he s ystem model derived from a knowledge of t he i nternal s tructure of the system is its i nternal description. In contrast, a n external description of a system is i ts description as seen from t he s ystem's i nput a nd o utput terminals; it can be obtained by a pplying a known input a nd measuring the resulting o utput. I n t he m ajority of p ractical systems, a n e xternal description of a system so obtained is equivalent t o i ts i nternal description. In some cases, however, t he e xternal description fails t o give adequate information a bout t he system. Such is t he case with t he so-called uncontrollable or unobservable systems. References 1. 2. 3. 4. P apoulis, A ., T he Fourier Integral and Its Applications, McGraw-Hill, New York, 1962. K ailath, T ., L inear Systems, Prentice-Hall, Englewood Cliffs, New Jersey, 1980. L athi, B .P., Signals, Systems, and Communication, Wiley, New York, 1965. Lathi, B .P., Signals and Systems, Berkeley-Cambridge Press, Carmichael, California, 1987. Problems Find the energies of the signals illustrated in Fig. P I.I-I. Comment on the effect on energy of sign change, time shifting, or doubling of the signal. What is the effect on the energy if the signal is multiplied by k? 1 .1-2 Repeat Prob. 1.1-1 for the signals in Fig. P1.1-2. 1 .1-3 ( a) Find t he energies of the pair of signals x (t) and y(t) depicted in Figs. P l.l-3a and b. Sketch and find the energies of signals x (t) + y(t) and x (t) - y(t). Can you make any observation from these results? 97 Problems (b) (a) ( d) (c) sintr\ F ig. P l.l-l f (t) 0 O t- ~ o 2 t- f 3 ( t) 1 o 2 t- 0 -1 F ig. P l.l-2 x (t) ~ o 0 2 (a) x (t) 0 1 1- -1 1- y (l) t- 0 I- (b) x (t) y (t) 1 .1-1 I- (c) 0 It I- Fig. P l.l-3 ( b) Repeat part (a) for the signal pair illustrated in Fig. P1.1-3e. Is your observation in p art (a) still valid? 98 1 .1-4 1 I ntroduction t o S ignals a nd S ystems 99 P roblems F ind t he p ower o f t he p eriodic signal f (t) s hown in Fig. P1.1-4. F ind also t he powers a nd t he r ms values of: ( a) - f(t) ( b) 2 f(t) ( c) c f(t). C omment. f (1) 0.5 o 1- 24 -I ..... t- F ig. P 1.3-2 Fig. P l.l-4 1 .1-5 S how t hat t he p ower o f a signal 1- n f (t) = L Dke jwkt is Fig. P 1....
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