Question

x(n)=2cos((pie/4)n)+cos((3*pie/4)n)

implement in matlab the filtering problem

Answer 1

clear all
clc

%% samples duration
n=0:1:100;
%% Input signal generation
x = 2*cos((pi/4).*n) + cos((3*pi/4).*n);
%% plot the response
figure(1)
stem(n,x)
grid on
xlabel('n')
ylabel('x[n]')
title('Discrete signal response')

%% band pass filter design
order = 6;
f_lc = 0.2; % lower cutoff
f_hc = 0.6; % higher cutoff
%% design the filter
[b,a] = butter(order,f_lc/(f_hc/2));
freqz(b,a)
%% filtering response
y = filter(b,a,x);
%% plot the output response
figure(2)
stem(n,y)
grid on
xlabel('n')
ylabel('y[n]')
title('Filtered response of the output signal')

The original signal response is shown below

The filter response is shown below

The filtered signal response is shown below