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Obtain the exponential Fourier series for the signal in Fig. 17.54.
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Find the exponential Fourier series for the signal in Figure 17.54.
Answer to Problem 11P
The exponential Fourier series
Explanation of Solution
Given data:
Refer to Figure 17.54 in the textbook.
Formula used:
Write the expression to calculate the fundamental angular frequency.
Here,
Write the general expression to calculate exponential Fourier series of
Here,
Write the expression to calculate exponential Fourier series coefficients.
Calculation:
The given waveform is drawn as Figure 1.
Refer to Figure 1. The Fourier series function is defined as,
The time period of the function in Figure 1 is,
Substitute
Substitute
Simplify the above equation to find
Simplify the above equation to find
Assume the following to reduce the equation (4).
Substitute the equations (5) in equation (4) to find
Consider the following integration formula.
Compare the equations (5) and (7) to simplify the equation (5).
Using the equation (7), the equation (5) can be reduced as,
Simplify the above equation to find
Simplify the above equation to find
Substitute
Substitute
Conclusion:
Thus, the exponential Fourier series
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Chapter 17 Solutions
EBK FUNDAMENTALS OF ELECTRIC CIRCUITS
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