RR_ALPHA - Sensitivity of the alpha parameter

Description

Reproducible research addendum for phase recovery problem

AN EXTENDED GRIFFIN LIM ALGORTITHM

Paper: Perraudin Nathanael, Balazs Peter

Demonstration matlab file: Perraudin Nathanael

ARI -- April 2013

Dependencies

In order to use this matlab file you need the LTFAT toolbox. You can download it on http://ltfat.sourceforge.net

The problem

From a spectrogram S, we would like to recover the signal with the closest spectrogram.

The problem could be written in the form:

with

• \(S\) : The original spectrogram
• \(G\) : A frame
• \(x\) : The signal we would like to recover

Note that for these simulations, we know that it exist one x such that \(|Gx|=S\).

Algorithms for solving the problem

We will compare 2 different algorithms to solve the problem

• Griffin-Lim : Original algorithm designed by griffin and Lim
• Forward-PBL : A modification of the Griffin-Lim

Goal of these simulations

Observe the role of the parameter 'alpha' in th Foward-PBL algorithm.

• For 'alpha'=0, we recover the Griffin lim algorithm
• For 'alpha'>1, the algorithm is usually unstable
• The optimum seems to be 'alpha'close to 1.

Results

Different values of 'alpha' on 'gspi'

Different values of 'alpha' on 'bat'

This code produces the following output:

LTFAT version 2.1.1. Copyright 2005-2015 Peter L. Søndergaard. For help, please type "ltfathelp". LTFAT is using the MEX backend.
(Your global and persistent variables have just been cleared. Sorry.)
R2p started
-- Create the windows and the operators...  Done
-- Create the spectrogram muliplier...  Done
-- Reconstruction method:GLA
   * The obtained ssnr is: 29.0263
-- Reconstruction done
-- Reconstruction method:FGLA  with alpha = 0.2
   * Selected method: fast Griffin-Lim algorithm
   * The obtained ssnr is: 30.3708
-- Reconstruction done
-- Reconstruction method:FGLA  with alpha = 0.7
   * Selected method: fast Griffin-Lim algorithm
   * The obtained ssnr is: 46.7171
-- Reconstruction done
-- Reconstruction method:FGLA  with alpha = 0.9
   * Selected method: fast Griffin-Lim algorithm
   * The obtained ssnr is: 15.2788
-- Reconstruction done
-- Reconstruction method:FGLA  with alpha = 0.99
   * Selected method: fast Griffin-Lim algorithm
   * The obtained ssnr is: 62.8824
-- Reconstruction done
-- Reconstruction method:FGLA  with alpha = 1
   * Selected method: fast Griffin-Lim algorithm
   * The obtained ssnr is: 34.256
-- Reconstruction done
-- Reconstruction method:FGLA  with alpha = 1.05
   * Selected method: fast Griffin-Lim algorithm
   * The obtained ssnr is: 12.335
-- Reconstruction done
-- Reconstruction method:FGLA  with alpha = 1.2
   * Selected method: fast Griffin-Lim algorithm
   * The obtained ssnr is: 6.66295
-- Reconstruction done
-- Display the results...  Done
-- Create the windows and the operators...  Done
-- Create the spectrogram muliplier...  Done
-- Reconstruction method:GLA
   * The obtained ssnr is: 8.06796
-- Reconstruction done
-- Reconstruction method:FGLA  with alpha = 0.2
   * Selected method: fast Griffin-Lim algorithm
   * The obtained ssnr is: 8.16456
-- Reconstruction done
-- Reconstruction method:FGLA  with alpha = 0.7
   * Selected method: fast Griffin-Lim algorithm
   * The obtained ssnr is: 8.47719
-- Reconstruction done
-- Reconstruction method:FGLA  with alpha = 0.9
   * Selected method: fast Griffin-Lim algorithm
   * The obtained ssnr is: 9.13363
-- Reconstruction done
-- Reconstruction method:FGLA  with alpha = 0.99
   * Selected method: fast Griffin-Lim algorithm
   * The obtained ssnr is: 11.1692
-- Reconstruction done
-- Reconstruction method:FGLA  with alpha = 1
   * Selected method: fast Griffin-Lim algorithm
   * The obtained ssnr is: 13.1296
-- Reconstruction done
-- Reconstruction method:FGLA  with alpha = 1.05
   * Selected method: fast Griffin-Lim algorithm
   * The obtained ssnr is: 7.93617
-- Reconstruction done
-- Reconstruction method:FGLA  with alpha = 1.2
   * Selected method: fast Griffin-Lim algorithm
   * The obtained ssnr is: 6.58507
-- Reconstruction done
-- Display the results...  Done