Wavelet transform,STFT, freq. localization

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The discussion centers on the concept of frequency localization in signals, particularly comparing a standard signal with four spectral components to a chirp signal composed of the same components. It is suggested that in a chirp, the instantaneous frequency changes over time, leading to a situation where not all spectral components are present simultaneously. The user questions this idea, asserting that all four spectral components are always present throughout the duration of the chirp. Clarification is sought on the concept of frequency localization, with wavelets and Short-Time Fourier Transform (STFT) mentioned as tools for analyzing local spectral content. The response emphasizes the need to clarify the nature of the chirp, indicating that it cannot consist solely of four frequency components.
fisico30
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hello Forum,

taken a signal 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.
IT is said that if the chirp increases in frequency with time (meaning its instantaneous frequency), those 4 spectral, Fourier components will not be present in the signal all at the same time.
If the signal last 40 second, it is possible that the first 10 s are dominated by the lower frequency w1, and the last 10 second by the frequency w4...
They speak of frequency localization in time...

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

Any clarification on frequency localization please...

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

thanks
fisico30
 
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You need to understand what your chirp is. The chirp cannot consist of 4 frequency components only.
 

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