Should i use window with hop_size in Wavelet Transform or Discrete Wavelet Transform?

Question

I have a signal (audio - voice) with 1 second of duration with sample rate of 50000 Hz. It is big signal and I wish extract some features and apply pattern recognition or classification.

My question is if the Wavelet transform or Discrete Wavelet transform is a time frequency representation (or time scale). So I shoudn't use window in signal as a buffer or like STFT? Or I should use window like STFT with hop_size and apply to every window a wavelet transform?

I think STFT use window to localize signal in time and see frequency content. Wavelet doesn't need this approach.

I try to compare this feature extraction with well know mel frequency spectrogram or Mel-frequency cepstral coefficients (MFCCs).

Sorry if there is any answer on this, I haven't found it.

(taking advantage of the opportunity if anyone wants to explain to me how filter bank (or discrete wavelet) located spectral content in time. Is it property of convolution?)

Answer 1

Basically, an analysis linear filter-bank is composed of several branches of convolutive filters, each branch with its own hop. The theory consists in finding under which the filter-bank is invertible, how to design the filters and choose the hops.

Each level of a dyadic discrete wavelet transform is a filter-bank block with a hop size of $2$ (downsampling by $2$) and an implicit window determined from the envelope of the low-pass and high-pass filters of each branch. With multi-band wavelets, the hop is an integer $M\ge 2$. When you cascade the basic wavelet blocks, things get more intricate, as you will have iterated convolutions of the above filters (which are thus localized) and combinations of the undersampling rates: hop sizes of $2$, $4$, $8$, $2^L$. Therefore, discrete wavelets inherently have windows and hops, albethey of different shapes and sizes.

For speech, which I am not practitioner of, it is not uncommon to use several STFT with different lengths: short and longer windows. The overlapping sizes are often (as far as I know) $1/4$, $1/2$ or $3/4$ of the number of frequency bins.