Question

1. The impulse response of an ideal band pass filter is given by the equation: n=0 h(n)w2 sin(n w2) w1 sin (n w1) T nwW2 Using the above equation, write a Matlab program that implements an approximation for the band pass filter with cut-off frequencies (1-0.2π rad/sample and ω2-0.3π rad/sample. Set the order of the filter to 100 or 101. Use a Bartlett window here. Plot the frequency and phase responses of this digital filter. Hint use the bartlett Matlab command. Name this program as P1.m.

Do it using Matlab.

Answer 1

MATLAB code is given below in bold letters. copy this code and paste it in am m file and name it P1.m

clc;
close all;
clear all;

% define w1 and w2 as follows
w1 = 0.2*pi; w2 = 0.3*pi;

% define n as follows
N = 100;
n = 0:N; % this corresponds to 100th order filter

% deine the impulse response of the filter
h = w2/pi*sin(n*w2)./(n*w2) - w1/pi*sin(n*w1)./(n*w1);

% first sample is given below
h(1) = w2/pi - w1/pi ;

% bartlett window implementation
h = h.*bartlett(N+1)';

% frequency response of the filter with bartlett window
figure;freqz(h,1);grid on;
title('Frequency response of the filter with bartlett window');

Frequency response is plotted below

Frequency response of the filter with bartlett window -20 g -60 -80 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.91 Normalized Frequency(x rad/sample) 400 E200 400 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.91 Normalized Frequency (XT rad/sample)