Concept explainers
Find the Fourier series representation of the signal shown in Fig. 17.64.
Figure 17.64
Find the Fourier series representation of the signal shown in Figure 17.64.
Answer to Problem 26P
The Fourier series representation
Explanation of Solution
Given data:
Refer to Figure 17.64 in the textbook.
Formula used:
Write the expression to calculate the fundamental angular frequency.
Here,
Write the general expression to calculate trigonometric Fourier series of
Here,
Write the expression to calculate the dc component of the function
Write the expression to calculate Fourier coefficients.
Calculation:
The given waveform is drawn as Figure 1.
Refer to the Figure 1. The Fourier series function of the waveform is defined as,
The time period of the function in Figure 1 is,
Substitute
Substitute
Simplify the above equation to find
Substitute
Simplify the above equation to find
Simplify the above equation to find
Substitute
Simplify the above equation to find
Simplify the above equation to find
Substitute
Conclusion:
Thus, the Fourier series representation
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Chapter 17 Solutions
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