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the time domain Fourier Series approximation of square wave function for the following number of harmonics ?

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Jay Patel
Jay Patel 2018-5-16
关闭： Walter Roberson 2018-5-17
Compute the Fourier series of a function, r(t), plot the resulting approximation in terms of its spectral content and in time. The function is a periodic square wave of period T, duty cycle D, and amplitude A.
r(t)={█(A,0≤t≤D@0, D<t≤T)┤
This is the square wave we discussed in class. From this square wave, you are required to find the following:
  • A plot of the time domain Fourier Series approximation of this function for the following number of harmonics: n=5, n=10, n=50, n=100, n=200. You can assume A=1, T=0.001, D=0.00025.
  • Create a stem plot showing the amplitude of each of the first 100 harmonic values of An and Bn. Do this again for Cn.
  • Now that a time series representation of r(t) can be generated based upon the Fourier series coefficients, use this time series data, for n=5, n=10, n=50, n=100, n=200, to compute the FFT of the time series data. The output of this will be a stem plot showing you the spectral content of this time series. Compare these stem plots to the theoretical stem plots for the ideal square wave found in part 1b.

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