Wavelet transform,STFT, freq. localization

  • Thread starter Thread starter fisico30
  • Start date Start date
  • Tags Tags
    Wavelet
Click For Summary
SUMMARY

The discussion centers on the concept of frequency localization in signals, particularly comparing a standard signal composed of four spectral components with a chirp signal that also contains these components. It is established that in a chirp signal, the four Fourier components are not simultaneously present due to the nature of frequency modulation over time. The use of wavelet transforms and Short-Time Fourier Transform (STFT) is emphasized as essential tools for analyzing the local spectral content of such signals. The participant fisico30 highlights the misconception that a chirp can consist solely of four frequency components.

PREREQUISITES
  • Understanding of Fourier transforms and their properties
  • Knowledge of chirp signals and their characteristics
  • Familiarity with wavelet transforms and their applications
  • Experience with Short-Time Fourier Transform (STFT) analysis
NEXT STEPS
  • Research the principles of frequency modulation in chirp signals
  • Learn about the mathematical foundations of wavelet transforms
  • Explore the implementation of STFT in signal processing
  • Study examples of frequency localization in various signal types
USEFUL FOR

Signal processing engineers, researchers in time-frequency analysis, and anyone interested in the behavior of chirp signals and their spectral components.

fisico30
Messages
362
Reaction score
0
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
 
Engineering news on Phys.org
You need to understand what your chirp is. The chirp cannot consist of 4 frequency components only.
 

Similar threads

Fourier Transform vs Short Time Fourier Transform...
  • · Replies 5 ·
Replies
5
Views
4K
Units of Fourier Transform (CTFT) vs spectral density
  • · Replies 2 ·
Replies
2
Views
2K
Why does a series of pulses generate a pitch?
  • · Replies 27 ·
Replies
27
Views
5K
Smearing an audio recording using Fourier transform
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Regarding the Continous Wavelet Transform 'a' parameter
  • · Replies 1 ·
Replies
1
Views
2K
Help with understanding of RF theory-Kinetic inductance parametric amp
  • · Replies 1 ·
Replies
1
Views
2K
Engineering How Can MATLAB Be Used to Analyze Signal Duration and Frequencies Using DFT?
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad Could fast radio bursts be alien radar signals?
  • · Replies 9 ·
Replies
9
Views
1K
Op-amp compensation of cascade fudges audio signal oddly
  • · Replies 3 ·
Replies
3
Views
2K
Graduate How Do Wavelets Compare to Fourier Transforms for Analyzing Non-Uniform Signals?
  • · Replies 6 ·
Replies
6
Views
10K