Re: frequency localization...



On Oct 5, 4:42 pm, "fisico32" <marcoscipio...@xxxxxxxxx> wrote:
hello Forum,

given a time signal x(t) composed of 4 spectral components, with Fourier
angular frequencies w1 < w2< w3< w4.

Take now a completely different signal, a chirp, made of the same 4
spectral components (same power spectrum).
The phase spectrum of the two signal must be clearly different....

No. Contemplate how to design them to be the same..............


If the chirp increases in (instantaneous) frequency with time , those 4
spectral Fourier components will not be present in the signal all at the
same time....
for instance, if the signal lasted 40 second, the first 10 s would be
dominated by the lower frequency w1, and the last 10 second by the
frequency w4......

I would conjecture(1) that in general the power spectra are not the
same between the ganged and alternated cases for w's and interval as
constrained above.

I would conjecture(2) that for w's and interval constrained as above,
with equal power spectra, the phase spectra can be made the same.

Discuss......

They speak of frequency localization in time......


Who are they? Where do they speak? What do they say that you think is
interesting or relevant in this thread?

I would instead say that, also in the case of the chirp, the 4 spectral
components are present for the whole duration of the signal.....

Is this a homework problem? ...a big money bet on philosophical
semantics?


Any clarification on frequency localization please...

Any clarification on motivation or a question please........


wavelets and STFT are used to find the local spectral content in that
case.....

Wavelets and STFT can be calculated with many choices of impulse
response duration. Resolution in localization will depend on the
impulse response duration of the localizer and the durations of the
signal components to be localized(among other things).


thanks
fisico32

Dale B. Dalrymple
.