1. Purpose The purpose of this lab is to investigate FIR filtering with windows and apply it to a couple of practical problems. 2. Background Read Unit #3.5 3. Assignment I. Matlab function to display magnitude on a dB scale. The first part of the assignment is to write a quick Matlab function to display the magnitude (only) of the Fourier transform of a given sequence on a dB scale. function ph = magdb(h) % MAGDB Display magnitude of Fourier transform of h[n] on a dB scale. % ph = magdb(h) You did something similar in Lab #4, but here you will use the fft. Specifically, you should recognize that fft(h, N) is equivalent to taking the DTFT of , sampled at N point. You obviously have to choose N to be larger than the length of . Something like 1024 points is a nice number. You’ll plot it on a dB scale, so you can clearly see the stopband ripples. Here’s what you would get if you plotted the magnitude of a 21-pt FIR lowpass filter designed using a rectangular window to truncate the impulse response of an ideal LPF with a cutoff frequency of . The Matlab command would be magdb(fir1(20, 0.5, rectwin(21)).
Note that I’ve also superimposed a grey line on the plot to indicate the frequency response of the ideal lowpass filter. Also, I used the LineWidth and Color options in the plot command to give me a thick, blue line. You will also want to add a way so you can change the color of your plot, so you can eventually display several plots on the same axis, each with a different color and linewidth. One way would be to add input arguments to the function, for example function magdb(h, color, linewidth). But that’s a pretty crummy idea. A better way would be to have the function return a handle to the plot, which you can then manipulate. Here’s the outline of the function: function ph = magdb(h) % MAGDB Display magnitude of Fourier transform of h[n] on a dB scale. % ph = magdb(h) … bunch of code here resulting in array H, which is the magnitude of Fourier transform of h[n]…