Wavelet transform,STFT, freq. localization

[fisico30]

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

 

[0xDEADBEEF]

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

 

[oswaler]

I can provide some insights on the concept of frequency localization and how it relates to wavelet transform and STFT.

Frequency localization refers to the ability to identify the specific frequency components present in a signal at a particular time. This is important because many signals, such as the chirp mentioned in the content, have varying frequency components over time. In such cases, it is crucial to be able to accurately pinpoint when and at what frequency a particular component appears in the signal.

Wavelet transform and STFT are both signal processing techniques that are commonly used for frequency analysis. They both provide a way to analyze signals in the time-frequency domain, which allows for better localization of frequency components. Unlike the traditional Fourier transform, which only provides frequency information for the entire signal, wavelet transform and STFT provide frequency information at different time intervals, allowing for better localization.

In the case of the chirp signal, the lower frequency components may dominate in the first 10 seconds, while the higher frequency components may dominate in the last 10 seconds. Wavelet transform and STFT can help identify and analyze these changes in frequency content over time, providing a more accurate understanding of the signal.

In conclusion, frequency localization is an important concept in signal analysis, and techniques like wavelet transform and STFT are valuable tools for achieving it. By providing time-frequency information, these techniques allow for a better understanding of signals with varying frequency components over time.