Is it possible to downsample (decimate) these signals?

[giorgi3092]

Hi, another problem I'd like some clarification on, although I have my own answers.

When downsampling is performed, sampling theorem should still be fulfilled. So, in the first problem, we can downsample to fs=4kHz and we still fulfill the sampling theorem (2000*2 = 4 kHz). And the decimation factor is 2.

How about the next 2 problems tho?
My thinking is that if we were to downsample those by any factor, aliasing would be inevitable, hence, they cannot be downsampled. Is this correct?

 

[FvM]

It's not correct. Read about bandpass sampling.

 

[weetabixharry]

I would say it is possible to decimate any of these signals. Whether or not the decimated signal contains any useful or usable information is a completely separate matter, in my opinion.

 

[FvM]

I would say it is possible to decimate any of these signals. Whether or not the decimated signal contains any useful or usable information is a completely separate matter, in my opinion.

Obviously that's not what the OP is asking for, although he should have mentioned recoverability of the original signal. The questions are popular exercise problems and have meaningful and well defined answers.