Question regarding interpolation and decimation

Hi, I was tasked with the following question:

Construct a DT signal given by

• Sketch the signal using the stem function.
• Transform the signal x[k] based on the operation y[k] = x[k/5] followed by the operation z[k] = y[5k]. What is the relationship between x[k] and z[k]?
• Repeat (ii) with the order of interpolation and decimation reversed.

So far I've solved (i) and (ii) (code and result attached). Is what I'm doing correct? I also need help understanding the (iii) as I simply do not get what is being asked. Please let me know if what I have solved is correct and that what is being asked in (iii).

clc;
close all;
clear all;

% Variables
k = [0:1:120];
x = (1 - exp(-0.003 * k) .* cos((pi * k) / 20));
N = length(x);
n = 0:N-1;

% Question I
subplot(3,1,1)
stem(n, x);
xlabel('Samples');
ylabel('Amplitude');
title('Input Sequence');

% Question II
y = x(1:5:120);
n1 = 0:length(y)-1;
subplot(3,1,2)
stem(n1, y);
xlabel('Samples');
ylabel('Amplitude');
title('Decimated Sequence');

z = zeros(1,5*N);
n2 = 1:1:5*N;
j = 1:5:5*N;
z(j) = x;
subplot(3,1,3)
stem(n2, z);
xlabel('Samples');
ylabel('Amplitude');
title('Interpolated Sequence');

Answer 1

[Ananya Tewari]

Hi,

You can refer to the documentation of interpolation and decimation to understand about them. Here is the link to another answer which may help you in getting a better understanding of interpolation, decimation and their implementation.