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Midterm3SampleProblems.solutions

Midterm3SampleProblems.solutions - 1 Compute the complex...

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Unformatted text preview: 1. Compute the complex exponential Fourier series coefficients . Solution We seek the coefficients for the series expression However, note that which is already in the correct form. Thus . 2. Find the fundamental period of Solution 3. Compute the complex exponential Fourier series coefficients over one period as . Solution . , for the periodic signal and for all and for the periodic signal defined For Recall that and thus . Therefore, Note that if even, then and if is odd, then . Note also that for any is an odd number. Thus integer , is an even number and For the case that , and for the periodic signal 4. Compute the complex exponential Fourier series coefficients Solution The fundamental period is . shown below 5. Compute the Fourier transform of the signal 1.5 1 0 0 2 4 Solution First, we write as a sum of canonical rectangle functions, where the Fourier transform of is . Then we apply the relationships for time‐shifting and time‐scaling to write the answer directly, and Thus ...
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