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Properties of the Fourier Series

February 2, 2019 by 3200 Creative

Properties of the Fourier Series

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  1. Question 1 of 4
    1. Question

    A periodic signal x(t) has Fourier series coefficients X[k]. If y(t)=x(t+5), what are Y[k]? The period of both signals is T=20 sec.

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  2. Question 2 of 4
    2. Question

    You form the Fourier series coefficients Z[k] for a signal z(t) as Z[k]=0.5X[k+1]+0.5X[k-1]. How is z(t) related to x(t)? Assume both z(t) and x(t) have the same period of T=1 sec.

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  3. Question 3 of 4
    3. Question

    You form a signal z(t)=x^2(t). How are the Fourier series coefficients Z[k] related to X[k]?

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  4. Question 4 of 4
    4. Question

    A signal with period T=2 has Fourier series coefficients X[k] = \left\{\begin{array}{cl} 1,&k=\pm 2, \pm 4\\0& k\ne\pm 2, \pm 4 \end{array}\right.. What is the value of c=\int_0^2|x(t)|^2 dt?

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