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Fourier Series of the Square Wave and the Sinc Function

February 2, 2019 by 3200 Creative

Fourier Series of the Square Wave and the Sinc Function

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  1. Question 1 of 4
    1. Question

    One period of a square wave  x(t) is given by x(t)=\left\{\begin{array}{cl} 1,&|t|\le 5\\0,&5< |t|\le 20 \end{array}\right. . Identify the Fourier series coefficients  X[k].

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  2. Question 2 of 4
    2. Question

    If  x(t)=10 sinc (20t), what is  x(0) ?

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  3. Question 3 of 4
    3. Question

    The size of the peak ripple associated with Gibbs’ phenomena decreases proportional to  1/J for a  J harmonic Fourier series approximation to the square wave.

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  4. Question 4 of 4
    4. Question

    One period of a square wave x(t) is given by x(t)=\left\{\begin{array}{cl}1,&|t|\le \alpha\\0,&\alpha< |t|\le\beta \end{array}\right. . What happens to the Fourier Series coefficient  X[0] as \alpha/\beta decreases?

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