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

# For systems with memory also known as dynamic systems

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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....
View Full Document

## This note was uploaded on 04/14/2013 for the course ENG 350 taught by Professor Bayliss during the Spring '13 term at Northwestern.

Ask a homework question - tutors are online