Consequences of treating a periodic signal as aperiodic and vice versa?

[laskin]

Hi everybody, I am relatively new to DSP and completely new to this forum, as you can see. I am a masters student in neuroscience and am in the process of collecting electrophysiological data from the rat brain. In the brain there certainly is oscillatory activity which is periodic, but there also is activity which is aperiodic. I'm currently designing Matlab scripts to analyze my data and am using the fast Fourier transform for constructing periodograms and similar things. My question is, would this be adequate if the signal was aperiodic? I guess then I should use a DTFT analysis instead. What kinds of errors would I make if I analyze a signal which is aperiodic as if it were periodic? What about treating a periodic signal as aperiodic?

Thank you in advance for your help!

 

[Y.SAI SARASWATHI]

fft can be applied to both periodic and aperiodic signals if you time limit the signal,the difference is that spectrum of aperiodic is extended infinitely.(dtft analysis may not be required)

 

[laskin]

Thank you for your response! Let me see if I understood it correctly. If I apply dtft to a periodic signal, I should get an infinite frequency spectrum with only a finite number of frequencies having non-zero values, while the remaining ones will all be zero. Is that correct? If that's the case what would then be the consequence if I applied a DFT to an aperiodic signal? Will I simply be missing some information about the frequency domain?

Another thing, by time limiting the signal do you mean to simply not have an infinitely long signal? But aren't all signals we ever obtain finite?

Lastly, when should I use dtft instead of dft? Related to this, in many books showing, say, how to calculate coherence between two signals, they always use dtft in calculating spectra and cross-spectra. Is this just being more general, or is there a problem if I used dft instead for the same thing?

 

[Y.SAI SARASWATHI]

No,for a periodic signal spectrum will be discrete,if it is discrete periodic signal then spectrum will be periodic else if it is continuous periodic signal spectrum will be periodic.
know that when dtft is sampled in order to be processed by any digital system then it becomes dft(matlab terms it as fft although it actually performs dft using some efficient algorithms hence named so)
yes using dft some information about frequency spectrum will be lost hence we have to choose N as large as possible.
Time limiting is not considered in that way,it is true that all are time limited signals,but for analysis of periodic signals which we assume to be repetitive for infinite time we have to consider in that way.
for more information check signals and systems book by B.P.Lathi OXFORD Publications.