Wavelet

Comparison between Fourier transform, short-time Fourier transform and wavelets

Comparison between Fourier transform, short-time Fourier transform and wavelets
  1. What is the difference between STFT and wavelet transform?
  2. Why wavelet transform is better than short time Fourier transform?
  3. What is the difference between short time Fourier transform and Fast Fourier transform?
  4. What is the main advantage of wavelet analysis over STFT?

What is the difference between STFT and wavelet transform?

In contrast to the standard STFT which uses a single window size, the wavelet transform (WT) uses short windows at high frequencies and long windows at low frequencies [21]. Wavelets rely on the use of a mother wavelet function that can be scaled and shifted, to correlate with the anomalies or events of the signals.

Why wavelet transform is better than short time Fourier transform?

The result of the wavelet transform differs from the STFT in that its time-frequency resolution is not fixed and depends on the frequency (multi-scale property, see Fig. 5). In general, the wavelet transform represents lower frequency components with finer frequency resolution and coarser time resolution.

What is the difference between short time Fourier transform and Fast Fourier transform?

STFT provides the time-localized frequency information for situations in which frequency components of a signal vary over time, whereas the standard Fourier transform provides the frequency information averaged over the entire signal time interval.

What is the main advantage of wavelet analysis over STFT?

Wavelet analysis overcomes the disadvantage of STFT since CWT uses a windowing technique with variable sized regions. Wavelet analysis allows the use of long time intervals where we want more precise low-frequency information, and shorter regions where we want high-frequency information.

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