2. Pick a mean and standard deviation for a 1D Gaussian function f(x). a) Create plots of f(x) and its Fourier transform

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2 Pick A Mean And Standard Deviation For A 1d Gaussian Function F X A Create Plots Of F X And Its Fourier Transform 1 (34.57 KiB) Viewed 42 times

2. Pick a mean and standard deviation for a 1D Gaussian function f(x). a) Create plots of f(x) and its Fourier transform F(u) with properly labeled axes. (Use cycles per length as the frequency unit.) Identify the origin [zero (or DC) frequency]. What is the Nyquist frequency based on your discretization of f? b) Use the discrete form of the convolution theorem to compute the convolution of your function with itself when no zero-padding is used. Compare your result to what is obtained by convolving the continuous function and then sampling (the "truth"). c) Perform the numerical convolution using zero-padding. Compare your result to the truth.