I would like to know if there is any difference between the two purely from a DFT computation:
a) DFT of a signal
b) DFT of an impulse response of a LTI system
I assume both give insight into the frequency components (in case of a) and frequency response.
Appreciate comments from forum members
Nope, it's the same DFT, whether you are applying it to a signal or an impulse response.
thanks
Yeah, it stems from the continuous system H(s): the transfer function H(s) is the Laplace transform of the impulse response, and H(jw) is the Fourier transform of the impulse response.
Hi. Just to add my 'two cents': A discrete sequence has a DFT (a discrete spectrum). A system (such as a digital filter, differentiator, Hilbert transformer, etc.) has a frequency response. To avoid confusion, the words "spectrum" and "frequency response" should never be used interchangably.
Thanks. I did not realize this.
One issue is that you are free to window a signal vector to avoid sharp phase discontinuity and so get rid of false high frequencies but you should not window an impulse response when you analyse frequency response of a given system.
Ok. So, typically windowing is applied to incoming samples before they are passed to filer? Though in practical designs, I have not seen anyone implementing window function. I am wondering why ...
when you filter a signal you just filter it. Your question is not applicable.
My point of windowing before DFT applies if you want to assess frequency spectrum of a signal...
ok. thanks
Windowing is applied to signals before you do a DFT for spectral analysis. It is not, in general, applied before filtering.
ok. thanks
Since everyone's diving in:
It is the same DFT. It is the same because the impulse response of a linear, time-invariant system contains all the information that can ever be about that system (note that it doesn't necessarily tell you everything about some real system, because they're never completely linear or time invariant -- that's a screed for another day).
the calculation would be the same, but there may be times when you would prefer to scale the result so that the data corresponds to a value you are trying to measure, such as the signal RMS of a frequency bin in a power spectrum. this isn't functionally different than just computing the DFT, but it can be useful when graphing the spectrum of a signal
