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for a signal does freq spectrum change with time ?

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ciitv

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hi,
i know that for a given signal, there exists a corresponding freq spectrum. but i'm am baffled by my thought. can somebody explain this:
imagine this time domain signal: 10*sin(wt)u(-t)+5sin(wt)u(t)..i.e.sinusoidal signal is at one amplitude for -inf to 0 and another amp for 0 to +inf and freq remains the same. i know that for a given time domain a corresponding time invariant freq domainl exists... does the freq domain change at time=0 ?
 

Hi,
If you look at your signal from minus inf. to inf. you see a frequency spectrum for it. it's the frequency response of your whole signal. the question is, can we see a sudden changing of local frequency in t=0 directly with my whole signal spectra and interpret it. your answer is no. but what is solution?. the main general approach for solving this problem is to look (ans process) our signal locally and with shifting in Time. => Time-Frequency Transforms.
one of solution is Short Time Fourier Transform (STFT). Ther are some other solutions like Wigner-Ville Trans., Wavelet Trans. (CWT & DWT).

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    ciitv

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