Determine the impulse response of the system of part a). Now calculate the outpu

Question

Determine the impulse response of the system of part a). Now calculate the output of

the system using this impulse response via convolution using the function

conv().

use the

fft() command to estimate the frequency response of this system. Set the

arguement N in the fft (see the help for what N means) equal to 512. Write a program

that accepts the impulse response from part b), uses the fft as previously stated, and plot

the magnitude

(in dB) and phase of the frequency response.

Use the unwrap() command on the phase prior to plotting

Thanks for your help!

Explanation / Answer

he functions Y=fft(x) and y=ifft(X) implement the transform and inverse transform pair given for vectors of length N by: where is an Nth root of unity. Description Y = fft(X) returns the discrete Fourier transform (DFT) of vector X, computed with a fast Fourier transform (FFT) algorithm. This notation uses i for the imaginary unit, p and j for indices that run from 0 to m–1, and q and k for indices that run from 0 to n–1. The indices p+1 and j+1 run from 1 to m and the indices q+1 and k+1 run from 1 to n, corresponding to ranges associated with MATLAB arrays. The MATLAB function fft2 computes two-dimensional DFTs using a fast Fourier transform algorithm. Y = fft2(X) is equivalent to Y = fft(fft(X).').', that is, to computing the one-dimensional DFT of each column X followed by the one-dimensional DFT of each row of the result. The inverse transform of the two-dimensional DFT is computed by ifft2. The MATLAB function fftn generalizes fft2 to N-dimensional arrays. Y = fftn(X) is equivalent to: Y = X; for p = 1:length(size(X)) Y = fft(Y,[],p); end If X is a matrix, fft returns the Fourier transform of each column of the matrix. If X is a multidimensional array, fft operates on the first nonsingleton dimension. Y = fft(X,n) returns the n-point DFT. fft(X) is equivalent to fft(X, n) where nis the size of X in the first nonsingleton dimension. If the length of X is less than n, X is padded with trailing zeros to length n. If the length of X is greater than n, the sequence X is truncated. When X is a matrix, the length of the columns are adjusted in the same manner. Y = fft(X,[],dim) and Y = fft(X,n,dim) applies the FFT operation across the dimension dim.

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