DSP - Aliased Signals

[redboots]

Hi all,

I have included a photo of a homework problem for an Intro to Digital Signal Processing course. I am getting confused on parts C and D. Does anyone have any assistance? In part C, I was getting wa = 66.67(pi) but I think I am wrong.

 

[(*steve*)]

For part C you have given a single value. Do you think there is just one solution?

An incomplete solution would have all the values equal to zero.

For a 20Hz sample frequency, the signal frequency could be 10Hz, 20Hz, 30Hz,...

For a 50Hz sample frequency, the signal frequency could be 25Hz, 50Hz, 75Hz,...

Now, if the signal frequency is the same, then the valid signal frequencies can only be those frequencies in common. Clearly this is also a sequence.

And since the answer is a frequency, it must be in units of 1/seconds. This could be Hz or radians/sec.

There may be other answers where the sample values are not zero, but I'll leave this up to you.

 

[redboots]

No, I don't think there is just one solution to part C. Sorry, I should've explained better. What do you mean by "An incomplete solution would have all the values equal to zero."? What are you referencing by "all the values"?

 

[redboots]

Steve, do you mean wa=wb=0? Once you move to part D, you can see that answer is not accepted. Let me show you what I did on Part C. I believe it to be wrong because it doesn't lead to the correct number of responses for Part D where, according to my method in C, I only found when wa = 66.67*pi (letting l=1) to be between 0 < wa < 70*pi.

 

[(*steve*)]

What I mean is that it's a solution for a[n] == b[n], wa == wb, but with a[n] == 0.

This is a subset of the solution for part C, and I only gave it to illustrate that your answer will be a series.

You're already aware of this, so it wasn't much help.

Once you have a series, you should be able to manually check a few points. Whilst tho won't guarantee that your answer is complete, it will allow you to test whether the answer you've given is plausible.