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For the function given in figure below, derive the expressions of coefficients and sketch the Fourier amplitude spectra for the first four nonzero terms if A = 3, To = 8 ms.

For the function given in figure below, derive the expressions of coefficients and sketch the Fourier amplitude spectra for the first four nonzero terms if A = 3, To = 8 ms.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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For the function given in figure below, derive the expressions of coefficients and sketch the Fourier amplitude spectra for the first four nonzero terms if A = 3, To = 8 ms.
Transcribed Image Text:For the function given in figure below, derive the expressions of coefficients and sketch the Fourier amplitude spectra for the first four nonzero terms if A = 3, To = 8 ms.
Expert Solution
Step 1

As the given signal is an even signal, the 0th Fourier series coefficient is zero as well as the bn term is zero.

Write the expression for the function in the interval 0 to T0/2.

Electrical Engineering homework question answer, step 1, image 1

Step 2

Calculate the an coefficient of the Fourier series.

Electrical Engineering homework question answer, step 2, image 1

Step 3

Integrate the above function using integration by parts with the proper limits.

Electrical Engineering homework question answer, step 3, image 1

Since, sin(πn) =0 for any n,

Electrical Engineering homework question answer, step 3, image 2

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