""" Name: inverseSTFT Date of Revision: Jun 2019 Programmer: Christian Dittmar, Yiğitcan Özer %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% If you use the 'NMF toolbox' please refer to: [1] Patricio López-Serrano, Christian Dittmar, Yiğitcan Özer, and Meinard Müller NMF Toolbox: Music Processing Applications of Nonnegative Matrix Factorization In Proceedings of the International Conference on Digital Audio Effects (DAFx), 2019. License: This file is part of 'NMF toolbox'. https://www.audiolabs-erlangen.de/resources/MIR/NMFtoolbox/ 'NMF toolbox' is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the the Free Software Foundation, either version 3 of the License, or (at your option) any later version. 'NMF toolbox' 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 'NMF toolbox'. If not, see http://www.gnu.org/licenses/. """ import numpy as np from scipy.fftpack import ifft from copy import deepcopy def inverseSTFT(X, parameter): """Given a valid STFT spectrogram as input, this reconstructs the corresponding time-domain signal by means of the frame-wise inverse FFT and overlap-add method described as LSEE-MSTFT in [2]. References ---------- [2] Daniel W. Griffin and Jae S. Lim, "Signal estimation from modified short-time fourier transform", IEEE Transactions on Acoustics, Speech and Signal Processing, vol. 32, no. 2, pp. 236-243, Apr 1984. Parameters ---------- X: array-like The complex-valued spectrogram matrix oriented with dimensions numBins x numFrames parameter: dict blockSize The blocksize to use during synthesis hopSize The hopsize to use during synthesis anaWinFunc The analysis window function reconstMirror This switch decides whether the mirror spectrum should be reconstructed or not appendFrame This switch decides whethter to compensate for zero padding or not synWinFunc The synthesis window function (per default the same as analysis window) analyticSig If this is set to True, we want the analytic signal numSamples The original number of samples Returns ------- y: array-like The resynthesized signal env: array-like The envelope used for normalization of the synthesis window """ # get dimensions of STFT array and prepare corresponding output numBins, numFrames = X.shape # initialize parameters parameter = init_parameters(parameter, numBins) reconstMirror = parameter['reconstMirror'] appendFrame = parameter['appendFrame'] analyticSig = parameter['analyticSig'] blockSize = parameter['blockSize'] hopSize = parameter['hopSize'] numPadBins = blockSize - numBins numSamples = numFrames * hopSize + blockSize # for simplicity, we assume the analysis and synthesis windows to be equal analysisWinFunc = deepcopy(parameter['winFunc']) synthesisWinFunc = deepcopy(parameter['winFunc']) # prepare helper variables halfBlockSize = round(blockSize / 2) # check if input parameters are complete if analysisWinFunc is None: analysisWinFunc = np.hanning(blockSize) if synthesisWinFunc is None: synthesisWinFunc = np.hanning(blockSize) # we need to change the signal scaling in case of the analytic signal scale = 2.0 if analyticSig else 1.0 # decide between analytic and real output y = np.zeros(numSamples, dtype=np.complex64) if analyticSig else np.zeros(numSamples, dtype=np.float32) # construct normalization function for the synthesis window # that equals the denominator in eq. (6) in [1] winFuncProd = analysisWinFunc * synthesisWinFunc redundancy = round(blockSize / hopSize) # construct hopSize-periodic normalization function that will be # applied to the synthesis window nrmFunc = np.zeros(blockSize) # begin with construction outside the support of the window for k in range(-redundancy + 1, redundancy): nrmFuncInd = hopSize * k winFuncInd = np.arange(0, blockSize) nrmFuncInd += winFuncInd # check which indices are inside the defined support of the window validIndex = np.where((nrmFuncInd >= 0) & (nrmFuncInd < blockSize)) nrmFuncInd = nrmFuncInd[validIndex] winFuncInd = winFuncInd[validIndex] # accumulate product of analysis and synthesis window nrmFunc[nrmFuncInd] += winFuncProd[winFuncInd] # apply normalization function synthesisWinFunc /= nrmFunc # prepare index for output signal construction frameInd = np.arange(0, blockSize) # then begin frame-wise reconstruction for k in range(numFrames): # pick spectral frame currSpec = deepcopy(X[:, k]) # if desired, construct artificial mirror spectrum if reconstMirror: # if the analytic signal is wanted, put zeros instead padMirrorSpec = np.zeros(numPadBins) if not analyticSig: padMirrorSpec = np.conjugate(np.flip(currSpec[1:-1], axis=0)) # concatenate mirror spectrum to base spectrum currSpec = np.concatenate((currSpec, padMirrorSpec), axis=0) # transform to time-domain snip = ifft(currSpec) # treat differently if analytic signal is desired if not analyticSig: snip = np.real(snip) # apply scaling and synthesis window snip *= synthesisWinFunc * scale # determine overlap-add position overlapAddInd = k * hopSize + frameInd # and do the overlap add, with synthesis window and scaling factor included y[overlapAddInd] += snip # check if borders need to be removed if appendFrame: y = y[halfBlockSize:len(y) - halfBlockSize] # check if number of samples was defined from outside if parameter['numSamples']: y = y[0:parameter['numSamples']] return y.reshape(-1, 1), synthesisWinFunc def init_parameters(parameter, numBins): """Auxiliary function to set the parameter dictionary Parameters ---------- parameter: dict See the above function inverseSTFT for further information Returns ------- parameter: dict """ parameter = dict() if not parameter else parameter parameter['blockSize'] = 2048 if 'blockSize' not in parameter else parameter['blockSize'] parameter['hopSize'] = 512 if 'hopSize' not in parameter else parameter['hopSize'] parameter['winFunc'] = np.hanning(parameter['blockSize']) if 'winFunc' not in parameter else parameter['winFunc'] parameter['appendFrame'] = True if 'appendFrame' not in parameter else parameter['appendFrame'] parameter['analyticSig'] = False if 'analyticSig' not in parameter else parameter['analyticSig'] # this controls if the upper part of the spectrum is given or should be # reconctructed by 'mirroring' (flip and conjugate) of the lower spectrum if 'reconstMirror' not in parameter: if numBins == parameter['blockSize']: parameter['reconstMirror'] = False elif numBins < parameter['blockSize']: parameter['reconstMirror'] = True return parameter