Digital Signal Processing question

Thread Starter

duff650

Joined Mar 15, 2019
38
I have a question from a past paper that I am struggling to get my head around. Computing the energies is simple enough, however when it comes to finding which signal is periodic (which is probably simple enough) I cant figure out how to do it. I understand that for a signal to be periodic,
x[k] = x[k + N]. The zero time index for each signal is indicated for both signals. I have tried to find N but each time I go through the working neither signal is periodic so I must have the wrong N value. Any help would be appreciated! I've tried drawing out both signals but that doesn't really help because of aliasing.

upload_2019-7-25_20-30-21.png
 

Thread Starter

duff650

Joined Mar 15, 2019
38
What could autocorrelation of the signals be expected to show?
for the function x2[n] I got

[16 16 0 16 32 0 16 64 16 0 32 16 0 16 16]

Because it is mirrored does that mean it is periodic?

EDIT:

for x1[n]

[144 144 144 144 0 144 576 144 0 144 144 144 144]

they are both mirrored not sure what I am supposed to be looking for

EDIT:

there is only 13 points in x1[n] correlation compared to 15 feel like im nearly there
 
Last edited:

RBR1317

Joined Nov 13, 2010
547
Here are correlation results using Maple to perform the calculations. Note it is often useful to normalize the signal amplitudes for correlation. A periodic signal in the sample will show as a periodic form in the correlation, whereas white noise will show no such variations in the auto-correlation. This can be easier to see by graphing the results.
 

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