Digital Signal Processing MATLAB Explanation of assignment; In this assignment,

Question

Digital Signal Processing MATLAB

Explanation of assignment;

In this assignment, you are required to load the provided music signal music1.wav as signal x into matlab. Load the music into matlab using:

[x,fs]=wavread(music1.wav);Here x is the sampled music signal and fs is the sampling rate of that signal. You should use this

sampling rate in your discrete-time filter designs. (fs = 16000)

-Always use a maximum passband attenuation of 0.2 dB and minimum stop- band attenuation of 45

dB in your filter designs.

-You may always assume a fixed 200 Hz between your passband and
stopband edge frequencies. If you cannot get a filter that can satisfy the specs, you may relax the
specs to make it possible to design the filter. For example, you may reduce 45 dB value or
increase 0.2 dB value. You may also extend the distance between passband and stopband edges.

Objectives

1)
a) Design a Butterworth IIR lowpass filter with cutoff around 600 Hz (i.e. 500 and 700 Hz as passband and stopband edges). You can use the “buttord” command to calculate the minimum order of a Butterworth filter. Please see MATLAB help for usage of this command.
b) Plot the amplitude and phase responses of these three filters. Also plot poles and zeros on the
z-plane.
c) Use the “filter” command to filter the input music signal x with the filter you designed above and obtain x1 signal. Listen using soundsc(x1,fs) command and comment on the
quality of the output music.

Here our signal properties, (fs = 16000) sampling frequency of our input signal.

Explanation / Answer

[x,fs] = wavread('music1.wav')

fs=16000;

fp=500;

fst=700;

rp=0.2;

rs=45;

wp=2*fp/fs;

ws=2*fst/fs;

[n,wn] = buttord(wp,ws,rp,rs);

[b,a]= butter(n,wn,'low');

freqz(b,a,600,fs);

title('magnitude and phase response')

zplane(b,a);

x1=filter(b,a,x);

soundsc(x1,fs)

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