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DEMO_FILTERBANKS - CQT, ERBLET and AUDLET filterbanks

Description

This demo shows CQT (Constant Quality Transform), ERBLET (Equivalent Rectangular Bandwidth -let transform), and AUDLET (Auditory -let) representations acting as filterbanks with high and low redundancies. Note that ERBLET and AUDLET are similar concepts. The main difference is that ERBlet uses only the perceptual ERB scale while AUDlet allows for various perceptual scales like Bark or Mel scales. In short, ERBFILTERS is a wrapper of AUDFILTERS for the ERB scale. Filterbanks are build such that the painless condition is always satisfied. Real input signal and filters covering only the positive frequency range are used. The redundancy is calculated as a ratio of the number of (complex) coefficients and the input length times two to account for the storage requirements of complex numbers.

  • The high redundancy representation uses 'uniform' subsampling i.e. all channels are subsampled with the same subsampling factor which is the lowest from the filters according to the painless condition rounded towards zero.
  • The low redundancy representation uses 'fractional' subsampling which results in the least redundant representation still satisfying the painless condition. Actual time positions of atoms can be non-integer, hence the word fractional.
demo_filterbanks_1.png

ERBLET representations

The high-redundancy plot (top) consists of 400 channels (~9 filters per ERB) and the low-redundancy plot (bottom) consists of 44 channels (1 filter per ERB).
demo_filterbanks_2.png

CQT representations

Both representations consist of 280 channels (32 channels per octave, frequency range 50Hz-20kHz). The high-redundany represention is on the top and the low-redundancy repr. is on the bottom.
demo_filterbanks_3.png

AUDLET representations

The first representation consists of 72 channels BARKlet FB (3 filters per Bark in the frequency range 100Hz-16kHz using fractional subsampling. The second representation consists of 40 channels MELlet FB using uniform subsampling and triangular windows.