Wavelet Transform and STFT

Question

How wavelet transform is different from STFT.

I'm not able to understand what is resolution in frequency domain means?

Answer 1

In the STFT, you apply windowing and Fourier transform on the signal using sliding patches and then combine the resulting transforms, which will help you eventually end up with a uniform time/frequency representation of the signal.

In the wavelet transform case, you apply a filter bank on the overall signal at once. In this way, you obtain a coarse-to fine resolution pattern on the time/frequency representation.

Both methods result in similar time/frequency representations which can be derived from each other.

The major differences: (1) STFT is uniform yet CWT is not. (2) You apply STFT on patches, but you apply CWT on the overall signal. (3) STFT involves Fourier transforms but CWT only requires an orthogonal filter bank.

Answer 2

Accepted answer is wrong:

1. DWT (actually CWT) plot y-axis must read frequency not scales; the two are inversely related.
2. CWT and STFT aren't equivalentlish-ly similar as suggested; the same plot illustrates their fundamental differences which bear numerous implications.
3. "STFT on patches but CWT on overall" - both are applied on patches.
4. "CWT only needs orthogonal filter bank" - this is confused with DWT; CWT produces an overcomplete representation with adjacent scales not orthogonal.

I recommend this tutorial on the topic and MATLAB docs on CWT.