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Suppose we are given the following information about a signal x[n]: 1. x[ n] is a real

Chapter 3, Problem 3.11

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QUESTION:

Suppose we are given the following information about a signal x[n]: 1. x[ n] is a real and even signal. 2. x[n] has period N = 10 and Fourier coefficients ak. 3. a11 = 5. 9 4. Yo 2:: jx[nJI2 = 50. n=O Show that x[ n] = A cos(Bn + C), and specify numerical values for the constants A, B, and C

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QUESTION:

Suppose we are given the following information about a signal x[n]: 1. x[ n] is a real and even signal. 2. x[n] has period N = 10 and Fourier coefficients ak. 3. a11 = 5. 9 4. Yo 2:: jx[nJI2 = 50. n=O Show that x[ n] = A cos(Bn + C), and specify numerical values for the constants A, B, and C

ANSWER:

Step 1 of 4

Consider that the sin x[n] is the signal that is real and even. From the property of the discrete time Fourier series the Fourier coefficient is of the form.

Consider the expression for the Parseval’s theorem.

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