9 The purpose of this problem is to use MATLAB to compute th

9. The purpose of this problem is to use MATLAB to compute the magnitude, phase, and total energy of a Fourier transform. a) Develop a MATLAB routine to plot the magnitude and phase of a given Fourier transform HGe). The input part of your program will, of course, require that you specify the particular Hie) of interest, but, once this is done, your program should not depend on the Fourier transform specified. You will need to select an appropriate range of frequencies for these plots. Test your program using the following three signals for a 4 (plot all three using the same range of frequencies): h (t) e ii) h(t) e alt b) Extend the MATLAB routine that you developed in part a) to find the approximate total energy in each of the signals, as well as to find the approximate frequency in rad sec below which 90% of the total signal energy is contained. c) Suppose you wanted to design a simple low-pass filter with a specified cutoff frequency. Assuming that you could choose the desired value of a and based on the total energy criterion alone, which impulse response would you choose? Why? Note: Problems 1-8 are each worth 10 points, problem 9a is worth 10 points, and problems 9b and 9c are together worth 10 points.

Solution

pplication of low pass filter in reconstruction %Image dimensions [N,M] = size(I0grey); %[height, width] %Sampling intervals dx = 1; dy = 1; %Characteristic wavelengths KX0 = (mod(1/2 + (0:(M-1))/M, 1) - 1/2); KX1 = KX0 * (2*pi/dx); KY0 = (mod(1/2 + (0:(N-1))/N, 1) - 1/2); KY1 = KY0 * (2*pi/dx); [KX,KY] = meshgrid(KX1,KY1); %Filter formulation lpf = (KX.*KX + KY.*KY < K0^2); %Filter Application rec = ifft2(lpf.*ff);