By Hsu H.P.

ISBN-10: 007163472X

ISBN-13: 9780071634724

ISBN-10: 0071634738

ISBN-13: 9780071634731

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**Example text**

54. Hint: Use Eqs. 99). 55. 56. 57. 58. 59. 61. 1 Introduction Two most important attributes of systems are linearity and time-invariance. In this chapter we develop the fundamental input-output relationship for systems having these attributes. It will be shown that the input-output relationship for LTI systems is described in terms of a convolution operation. The importance of the convolution operation in LTI systems stems from the fact that knowledge of the response of an LTI system to the unit impulse input allows us to find its output to any input signals.

51. (a) See Prob. 17. 52. 53. 54. Hint: Use Eqs. 99). 55. 56. 57. 58. 59. 61. 1 Introduction Two most important attributes of systems are linearity and time-invariance. In this chapter we develop the fundamental input-output relationship for systems having these attributes. It will be shown that the input-output relationship for LTI systems is described in terms of a convolution operation. The importance of the convolution operation in LTI systems stems from the fact that knowledge of the response of an LTI system to the unit impulse input allows us to find its output to any input signals.

50. Let x[n] be an arbitrary sequence with even and odd parts denoted by x,[n] and xJn], respectively. 51. Determine whether or not each of the following signals is periodic. If a signal is periodic , determine its fundamental period. 52. 53. (a) }: (b) }: x[k] = }: x[k] k=O k=no What is lJ(2t)? What is lJ[2n]? 54. 55. 56. Consider a continuous-time system with the input-output relation 1 T y(t)=T{x(t)}=- It+T/2 t-T/2 x(-r)d-r Determine whether this system is (a) linear, (b) time-invariant, (c) causal.

### Schaum's outline of signals and systems by Hsu H.P.

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