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I have a signal $s(t)$ of duration $T$ with limited bandwidth. In matlab, I use a sampling frequency $fs$ and I have $L=T*fs$. After, I have $r=ones(size(s))+s$. To have a limited bandwidth, I filter with a raised cosine filter: $rr=filter(h,1,r)$ with $h$ the raised cosine filter.

My question: What is the duration for the signal $rr$? Personnally I would have said $T$. How to prove that?

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  • $\begingroup$ Can you add more detail about your question? The duration of rr is given by its length, and by the definition of filter, it's equal to the length of r. $\endgroup$ – MBaz Feb 18 at 19:40
  • $\begingroup$ So the duration of $rr$ is $T$. I don't have more detail $\endgroup$ – user40645 Feb 18 at 20:16
  • $\begingroup$ What kind of proof are you looking for? $\endgroup$ – MBaz Feb 18 at 20:28
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I have a signal s(t) of duration T with limited bandwidth.

No, you don't.

A signal cannot be finite in both time and frequency at the same time. So the whole question about length in both domains comes down to how exactly you define it. Typically you need a criteria like "less than -100dB", "99.99% of the entire energy" or something like this.

These criteria are specific to your application. Maybe -40dB is plenty, maybe you need more than -200dB. Once you have a criteria defined you can apply it to your signals and determine the "lengths", but the result will always be tied to an application specific definition.

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