Matlab工具集介绍（一）：ltfat（The Linear Time/Frequency Toolbox）
线性时频变换工具集
主页：http://ltfat.sourceforge.net/
Introduction
The Linear Time/Frequency Toolbox (LTFAT) is a Matlab/Octave toolbox for doing time-frequency analysis. It is intended both as an educational and computational tool. The toolbox provides the basic Gabor, Wilson and MDCT transform along with routines for constructing windows (filter prototypes) and routines for manipulating coefficients
LTFAT is developed at CAHR, Technical University of Denmark, ARI, Austrian Academy of Sciences and LATP, Universite de Provence.
Features
- TF-transforms: Gabor, Wilson and windowed MDCT
- Basic Fourier and TF-analysis (unitary DFT, involution, twisted conv., symplectic Fourier transformation).
- All transforms have methods for generating perfect reconstruction systems.
- TF-Operators: Gabor multiplier and spreading representation
- GUI in Matlab to modify signals in the time-frequency domain.
- Sparse regression in the Gabor and WMDCT domain.
- Support for full length windows and finite length windows (FIR)
- Windows: Gauss, Hanning etc. Canonical dual and tight windows
- Spectrogram and reassigned spectrogram plots
- Filterbanks.
- Non-stationary (time-evolving) Gabor systems.
- Simple tools for working with coefficients (thresholding, N-term approx.)
- Demos demonstrating the use of the toolbox.
- Works in Matlab/Octave with a backend in C for greater speed.
- The toolbox is Free software, released under the GNU General Public License (GPLv3).
Documentation
You can read the documentation included in the M-files online
Publications
If you use the toolbox in a scientic work, please cite one of the LTFAT notes, 011 or 015, as appropriate. This will help in securing a continued development of the toolbox.
% LTFAT - Gabor analysis
%
% Peter L. Soendergaard, 2007.
%
% Basic Time/Frequency analysis
% TCONV - Twisted convolution.
% DSFT - Discrete Symplectic Fourier Transform
% ZAK - Zak transform.
% IZAK - Inverse Zak transform.
% COL2DIAG - Move columns of a matrix to diagonals.
% TFMAT - Matrix of transform or operator in LTFAT.
%
% Gabor systems.
% DGT - Discrete Gabor transform.
% IDGT - Inverse discrete Gabor transform.
% DGT2 - 2D Discrete Gabor transform.
% IDGT2 - 2D Inverse discrete Gabor transform.
% DGTREAL - DGT for real-valued signals.
% IDGTREAL - IDGT for real-valued signals.
%
% Wilson bases and MDCT.
% DWILT - Discrete Wilson transform.
% IDWILT - Inverse discrete Wilson transform.
% DWILT2 - 2-D Discrete Wilson transform.
% IDWILT2 - 2-D inverse discrete Wilson transform.
% MDCT - Modified Discrete Cosine transform.
% IMDCT - Inverse MDCT.
% MDCT2 - 2-D MDCT.
% IMDCT2 - 2-D inverse MDCT.
% WIL2RECT - Rectangular layout of Wilson coefficients.
% RECT2WIL - Inverse of WIL2RECT.
%
% Window functions.
% PGAUSS - Periodized Gaussian.
% PSECH - Periodized SECH.
% PHERM - Periodized Hermite functions.
% PBSPLINE - Periodized B-spline.
% FIRWIN - FIR windows (Hanning,Hamming,Blackman,...).
% FIRKAISER - FIR Kaiser-Bessel window.
% IIRPAR - Easy calculation of IIR parameters.
% FIR2IIR - Extend FIR window to IIR window.
% IIR2FIR - Cur IIR window to FIR window.
%
% Reconstructing windows
% GABDUAL - Canonical dual window.
% GABTIGHT - Canonical tight window.
% GABPROJDUAL - Dual window by projection.
% GABMIXDUAL - Dual window by mixing windows.
% WILORTH - Window of Wilson/MDCT orthonormal basis.
% WILDUAL - Riesz dual window of Wilson/MDCT basis.
%
% Time/Frequency operators.
% GABMUL - Gabor multiplier.
% GABMULEIGS - Eigenpairs of Gabor multiplier.
% GABMULAPPR - Best approximation by a Gab. mult.
% SPREADOP - Spreading operator.
% SPREADINV - Symbol of inverse spreading operator.
% SPREADADJ - Symbol of adjoint spreading operator.
% SPREADFUN - Symbol of best approximation to matrix.
% SPREADEIGS - Eigenpairs of Gabor multiplier.
%
% Conditions numbers.
% GABFRAMEBOUNDS - Frame bounds of Gabor system.
% GABRIESZBOUNDS - Riesz sequence/basis bounds of Gabor system.
% WILBOUNDS - Frame bounds of Wilson basis.
% GABDUALNORM - Test if two windows are dual.
%
% Reassignment and instantaneous time/frequency.
% INSTTFDGT - Instantaneous time/frequency from signal.
% INSTTFABS - Instantaneous time/frequency from spectrogram.
% INSTTFPHASE - Instantaneous time/frequency from phase.
% GABREASSIGN - Reassign positive distribution.
%
% Phase conversions
% PHASELOCK - Phase Lock Gabor coefficients to time.
% PHASEUNLOCK - Undo phase locking.
% SYMPHASE - Convert to symmetric phase.
%
% Lasso methods
% GABELITISTLASSO- Elitist lasso threshholding.
% GABGROUPLASSO - Group lasso threshholding.
% GABLASSO - Landweber lasso threshholding.
%
% Plots.
% SGRAM - Spectrogram based on DGT.
% RESGRAM - Reassigned spectrogram.
% INSTFREQPLOT - Plot of the instantaneous frequency.
% MAGRESP - Magnitude response plot.
% PHASEPLOT - Plot of STFT phase.
%
% For help, errors, suggestions etc. please send email to
% ltfat-help@lists.sourceforge.net
% This program is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
%
% This program is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with this program. If not, see <http://www.gnu.org/licenses/>.
