Question

Please answer the question and include matlab code and plots. Thank You

Problem 1: The operation of signal dilation or decimation or down-sampling is defined by y(n) = x(nM) in which the sequence x(n) is down-sampled by an integer factor M. Explore Matlab’s downsample command to implement the above equation. Now generate x(n) = sin(0.125πn), for −50 ≤ n ≤ 50. Decimate x(n) by a factor of 4 to generate y(n). Plot both x(n) and y(n) using subplot and comment on the results. Repeat the above using x(n) = sin(0.5πn), for −50 ≤ n ≤ 50. Qualitatively discuss the effect of down-sampling on signals.

Answer 1

n=-50:1:50
x=sin(0.125*pi*n)
subplot(211)
stem(n,x)
xlabel('n');ylabel('x(n)');xlim([-50,50])
title('x(n)=sin(0.125 pi n)')

M=4;m=-50:M:50
y1=downsample(x,M)
subplot(212)
stem(m,y1,'r');xlabel('n');ylabel('y(n)');xlim([-50,50]);
title('y(n)=x(nM) for M=4')

n=-50:1:50
x=sin(0.125*pi*n)
subplot(211)
stem(n,x)
xlabel('n');ylabel('x(n)');xlim([-50,50])
title('x(n)=sin(0.125 pi n)')

M=8;m=-50:M:50
y1=downsample(x,M)
subplot(212)
stem(m,y1,'r');xlabel('n');ylabel('y(n)');xlim([-50,50]);
title('y(n)=x(nM) for M=8')

+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

clc;close all;clear all;
n=-50:1:50
x=sin(0.5*pi*n)
subplot(211)
stem(n,x)
xlabel('n');ylabel('x(n)');xlim([-50,50])
title('x(n)=sin(0.5 pi n)')

M=4;m=-50:M:50
y1=downsample(x,M)
subplot(212)
stem(m,round(y1),'r');xlabel('n');ylabel('y(n)');xlim([-50,50]);
title('y(n)=x(nM) for M=4')

clc;close all;clear all;
n=-50:1:50
x=sin(0.5*pi*n)
subplot(211)
stem(n,x)
xlabel('n');ylabel('x(n)');xlim([-50,50])
title('x(n)=sin(0.5 pi n)')

M=5;m=-50:M:50
y1=downsample(x,M)
subplot(212)
stem(m,round(y1),'r');xlabel('n');ylabel('y(n)');xlim([-50,50]);
title('y(n)=x(nM) for M=5')