Fast spectrogram phase reconstruction using Local Weighted Sums

# LWS

### Fast spectrogram phase recovery using Local Weighted Sums

Author: Jonathan Le Roux -- 2008-2019

LWS is a C/C++ library for which this package is a Python wrapper.
A Matlab/Mex wrapper is also available.

Copyright (C) 2008-2019 Jonathan Le Roux

## Citing this code

If you use this code, please cite the following papers:

### Batch LWS

Jonathan Le Roux, Hirokazu Kameoka, Nobutaka Ono, Shigeki Sagayama,
"Fast Signal Reconstruction from Magnitude STFT Spectrogram Based on Spectrogram Consistency,"
in Proc. International Conference on Digital Audio Effects (DAFx), pp. 397--403, Sep. 2010.

@InProceedings{LeRoux2010DAFx09,
author =	 {Jonathan {Le Roux} and Hirokazu Kameoka and Nobutaka Ono and Shigeki Sagayama},
title =	 {Fast Signal Reconstruction from Magnitude {STFT} Spectrogram Based on Spectrogram Consistency},
booktitle =	 {Proc. International Conference on Digital Audio Effects (DAFx)},
year =	 2010,
pages =	 {397--403},
month =	 sep
}


### Online LWS, "No future" LWS

Jonathan Le Roux, Hirokazu Kameoka, Nobutaka Ono, Shigeki Sagayama,
"Phase initialization schemes for faster spectrogram-consistency-based signal reconstruction,"
in Proc. of ASJ Autumn Meeting, 3-10-3, Sep. 2010.

@InProceedings{LeRoux2010ASJ09,
author =	 {Jonathan {Le Roux} and Hirokazu Kameoka and Nobutaka Ono and Shigeki Sagayama},
title =	 {Phase Initialization Schemes for Faster Spectrogram-Consistency-Based Signal Reconstruction},
year =	 2010,
booktitle =	 {Proc. Acoustical Society of Japan Autumn Meeting (ASJ)},
number =	 {3-10-3},
month =	 mar
}


## Installation:

1. The easiest way to install lws is via pip:
pip install lws

1. To compile from source using cython (required if one modifies the code):
cd python
LWS_USE_CYTHON=1 make

1. To compile from source using the pre-generated c source file (which was obtained with cython):
cd python
make

1. Alternatively, one can first use cython to create a tarball, which can then be installed with pip:
cd python
make sdist
pip install dist/lws-1.2.6.tar.gz


Note: On Windows, the Microsoft Visual C++ Compiler for your version of Python needs to be installed. See this page for more details.

## Usage

import lws
import numpy as np

lws_processor=lws.lws(512,128, mode="speech") # 512: window length; 128: window shift
X = lws_processor.stft(x) # where x is a single-channel waveform
X0 = np.abs(X) # Magnitude spectrogram
print('{:6}: {:5.2f} dB'.format('Abs(X)', lws_processor.get_consistency(X0)))
X1 = lws_processor.run_lws(X0) # reconstruction from magnitude (in general, one can reconstruct from an initial complex spectrogram)
print('{:6}: {:5.2f} dB'.format('LWS', lws_processor.get_consistency(X1)))


## Options

lws_processor=lws.lws(awin_or_fsize, fshift, L = 5, swin = None, look_ahead = 3,
nofuture_iterations = 0, nofuture_alpha = 1, nofuture_beta = 0.1, nofuture_gamma = 1,
online_iterations = 0, online_alpha = 1, online_beta = 0.1, online_gamma = 1,
batch_iterations = 100, batch_alpha = 100, batch_beta = 0.1, batch_gamma = 1,
symmetric_win = True, mode= None, fftsize=None, perfectrec=True)

• awin_or_fsize: either the analysis window, or a window length (in which case the sqrt(hann) window is used); the analysis window should be symmetric for the computations to be correct.
• fshift: window shift
• L: approximation order in the phase reconstruction algorithm, 5 should be good.
• swin: synthesis window (if None, it gets computed from the analysis window for perfect reconstruction)
• look_ahead: number of look-ahead frames in RTISI-LA-like algorithm, 3 should be good.
• xxx_iterations, xxx_alpha, xxx_beta, xxx_gamma: number of iterations of algorithm xxx (where xxx is one of nofuture, online, or batch), and parameters alpha/beta/gamma of the decreasing sparsity curve that is used to determine which bins get updated at each iteration. Any bin with magnitude larger than a given threshold is updated, others are ignored (thresholds = alpha * np.exp(- beta * np.arange(iterations)**gamma))
• symmetric_win: determines whether to use a symmetric hann window or not
• mode: None, 'speech', or 'music'. This sets default numbers of iterations of each algorithm that seem to be good for speech and music signals. Disclaimer: your mileage may vary.
• fftsize: can be set longer than frame size to do 0-padding in the FFT. Note that 0-padding will be done symmetrically on the left and right of the window to enforce symmetry in the analysis window.
• perfectrec: whether to pad with zeros on each side to ensure perfect reconstruction at the boundaries too.

Three steps are implemented, and they can be turned on/off independently by appropriately setting the corresponding number of iterations:

• "no future" LWS: phase initialization using LWS updates that only involve past frames
• online LWS: phase estimation using online LWS updates, corresponding to a fast time-frequency domain version of RTISI-LA
• LWS: phase estimation using batch LWS updates on the whole spectrogram

## Remarks

1. The .cpp files are actually C code with some C99 style comments, but the .cpp extension is needed on Windows for mex to acknowledge the c99 flag (with .c, it is discarded, and -ansi used instead, leading to compilation errors)

2. Because the module is a C extension, it cannot be reloaded (see http://bugs.python.org/issue1144263). In Jupyter Notebooks, in particular, autoreload will not work, and the kernel has to be restarted.

## Acknowledgements

The recipe to wrap the LWS C code as a python module was largely inspired by Martin Sosic's post: http://martinsosic.com/development/2016/02/08/wrapping-c-library-as-python-module.html

## Project details

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