Subject: Re: Speech(or Phase) Reconstruction from Magnitude Spectrum From: Matt Flax <flatmax(at)MATT.FLAX> Date: Tue, 1 Feb 2005 22:19:56 +1100--8t9RHnE3ZwKMSgU+ Content-Type: text/plain; charset=us-ascii Content-Disposition: inline Hi, This topic is very signal processing, or DSP. You will find efficient solutions by discussing this on the music-dsp e-mail list : http://ceait.calarts.edu/mailman/listinfo/music-dsp Yes you are correct. You do want to 'complexify' the magnitude only signal. You are now going down a road which is well tread, let me propose another approach ... Rather then think about the instantaneous phase of the signal, consider how the signal will be processed in sequential blocks .... how do you combine blocks (windows) of processed signal ? You may want to look into the standard overlap add technique and combine it with your current direction. Back to your topic .... and in a slightly different approach ... This complexification can come in many standard forms. They include minimum phase, maximum phase, zero phase and also mixed phase. The 'phase' relates to how the signal energy is centered in the time domain. Say you do a zero phase realisation, then the overall signal power will fluctuate according to the STFT power in each Fourier block of data. So if you keep your block resolution small enough, you should be able to get a pretty good signal in the end .... this is in some way connected to the question ... "What is the best sized window required to represent speech ... ". The answer to that question must be, well, what do you want to represent best ?!(at)# and can be quite a complex issue ... I attach the opposite of what you want to do ... if you invert this one line algorithm then you will find your answer !!! Pretend the signal in the script is not in the time domain, but the frequency domain ... in other words whatever domain you put into the signal, you get out of the algorithm ... time -> time, frequency -> frequency, f(freq) -> f(freq) and so on.... Be careful and remember some signals are energy and some signals are power ... these are non-linearly related ... so step your algorithm carefully from reading in the data to writing it out ... Matt -- http://www.flatmax.org MFFM Bit Stream : http://sourceforge.net/projects/mffmbitstream/ Other Projects : http://sourceforge.net/search/?type_of_search=soft&words=mffm --8t9RHnE3ZwKMSgU+ Content-Type: text/plain; charset=us-ascii Content-Disposition: attachment; filename="complexSigToRealSig.m" %# Copyright 2004 Matt Flax <flatmax(at)ieee.org> %# This file is a stand alone tool for generating a zero phase %# signal from a complex time signal %# %# It 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 2 of the License, or %# (at your option) any later version. %# %# This file 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 have received a copy of the GNU General Public License %# along with this file, if not then please refer to www.gnu.org %# to gain access to the GNU GPL license. function [rSig,cSig]=complexSigToRealSig(complexSig) %# converts complexSig to rSig, with zero vector cSig returned. %# This function is a zero phase implementation. signal=ifft(sqrt(2*(abs(fft(imag(complexSig))).^2+abs(fft(real(complexSig))).^ 2))); rSig=real(signal); cSig=imag(signal); endfunction --8t9RHnE3ZwKMSgU+--