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Engineering and Tech / Signals and Systems 2 / Chapter 3 / Problem 3.31

Signals and Systems | 2nd Edition | ISBN: 9780138147570 | Authors: Alan V. Oppenheim, Alan S. Willsky, with S. Hamid

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Let x[n] = { ~: be a periodic signal with fundamental period N = 10 and Fourier series

Chapter 3, Problem 3.31

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QUESTION:

Let x[n] = { ~: be a periodic signal with fundamental period N = 10 and Fourier series coefficients ak. Also, let g[n] = x[n] - x[n - 1]. (a) Show that g[n] has a fundamental period of 10. (b) Determine the Fourier series coefficients of g[n]. (c) Using the Fourier series coefficients of g[n] and the First-Difference property in Table 3.2, determine ak for k -:/= 0.

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QUESTION:

Let x[n] = { ~: be a periodic signal with fundamental period N = 10 and Fourier series coefficients ak. Also, let g[n] = x[n] - x[n - 1]. (a) Show that g[n] has a fundamental period of 10. (b) Determine the Fourier series coefficients of g[n]. (c) Using the Fourier series coefficients of g[n] and the First-Difference property in Table 3.2, determine ak for k -:/= 0.

ANSWER:

Step 1 of 4

Given data:

The fundamental period is .

The given functions are,

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