Question regarding interpolation and decimation
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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).
k = [0:1:120];
x = (1 - exp(-0.003 * k) .* cos((pi * k) / 20));
N = length(x);
n = 0:N-1;
% Question I
% Question II
y = x(1:5:120);
n1 = 0:length(y)-1;
z = zeros(1,5*N);
n2 = 1:1:5*N;
j = 1:5:5*N;
z(j) = x;