Suppose we are given the following information about a signal x(t): 1. x(t) is real and

Chapter 3, Problem 3.8

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QUESTION:

Suppose we are given the following information about a signal x(t): 1. x(t) is real and odd. 2. x(t) is periodic with period T = 2 and has Fourier coefficients ak. 3. ak = 0 for lkl > I. 4. Ho2 ix(t)j 2 dt = 1. Specify two different signals that satisfy these conditions.

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QUESTION:

Suppose we are given the following information about a signal x(t): 1. x(t) is real and odd. 2. x(t) is periodic with period T = 2 and has Fourier coefficients ak. 3. ak = 0 for lkl > I. 4. Ho2 ix(t)j 2 dt = 1. Specify two different signals that satisfy these conditions.

ANSWER:

Step 1 of 4

Consider a signal x(t) that is real and odd, then by the property of the Fourier series, the Fourier series is of the form.

In case of the real signal the Fourier coefficient is,

From the given question.

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