'''@file sigproc.py contains the signal processing functionality The MIT License (MIT) Copyright (c) 2013 James Lyons Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. This file includes routines for basic signal processing including framing and computing power spectra. Author: James Lyons 2012 ''' import math import numpy def framesig(sig, frame_len, frame_step, winfunc=lambda x: numpy.ones((x, ))): ''' Frame a signal into overlapping frames. Args: sig: the audio signal to frame. frame_len: length of each frame measured in samples. frame_step: number of samples after the start of the previous frame that the next frame should begin. winfunc: the analysis window to apply to each frame. By default no window is applied. Returns: an array of frames. Size is NUMFRAMES by frame_len. ''' slen = len(sig) frame_len = int(round(frame_len)) frame_step = int(round(frame_step)) if slen <= frame_len: numframes = 1 else: numframes = 1 + int(math.ceil((1.0*slen - frame_len)/frame_step)) padlen = int((numframes-1)*frame_step + frame_len) zeros = numpy.zeros((padlen - slen,)) padsignal = numpy.concatenate((sig, zeros)) indices = (numpy.tile(numpy.arange(0, frame_len), (numframes, 1)) + numpy.tile(numpy.arange(0, numframes*frame_step, frame_step), (frame_len, 1)).T) indices = numpy.array(indices, dtype=numpy.int32) frames = padsignal[indices] win = numpy.tile(winfunc(frame_len), (numframes, 1)) return frames*win def deframesig(frames, siglen, frame_len, frame_step, winfunc=lambda x: numpy.ones((x, ))): ''' Does overlap-add procedure to undo the action of framesig. Args: frames the: array of frames. siglen the: length of the desired signal, use 0 if unknown. Output will be truncated to siglen samples. frame_len: length of each frame measured in samples. frame_step: number of samples after the start of the previous frame that the next frame should begin. winfunc: the analysis window to apply to each frame. By default no window is applied. Returns: a 1-D signal. ''' frame_len = round(frame_len) frame_step = round(frame_step) numframes = numpy.shape(frames)[0] assert numpy.shape(frames)[1] == frame_len, '''"frames" matrix is wrong size, 2nd dim is not equal to frame_len''' indices = (numpy.tile(numpy.arange(0, frame_len), (numframes, 1)) + numpy.tile(numpy.arange(0, numframes*frame_step, frame_step), (frame_len, 1)).T) indices = numpy.array(indices, dtype=numpy.int32) padlen = (numframes-1)*frame_step + frame_len if siglen <= 0: siglen = padlen rec_signal = numpy.zeros((padlen, )) window_correction = numpy.zeros((padlen, )) win = winfunc(frame_len) for i in range(0, numframes): #add a little bit so it is never zero window_correction[indices[i, :]] = (window_correction[indices[i, :]] + win + 1e-15) rec_signal[indices[i, :]] = rec_signal[indices[i, :]] + frames[i, :] rec_signal = rec_signal/window_correction return rec_signal[0:siglen] def magspec(frames, nfft): ''' Compute the magnitude spectrum of each frame in frames. If frames is an NxD matrix, output will be NxNFFT. Args: frames: the array of frames. Each row is a frame. nfft: the FFT length to use. If NFFT > frame_len, the frames are zero-padded. Returns: If frames is an NxD matrix, output will be NxNFFT. Each row will be the magnitude spectrum of the corresponding frame. ''' complex_spec = numpy.fft.rfft(frames, nfft) return numpy.absolute(complex_spec) def powspec(frames, nfft): ''' Compute the power spectrum of each frame in frames. If frames is an NxD matrix, output will be NxNFFT. Args: frames: the array of frames. Each row is a frame. nfft: the FFT length to use. If NFFT > frame_len, the frames are zero-padded. Returns: If frames is an NxD matrix, output will be NxNFFT. Each row will be the power spectrum of the corresponding frame. ''' return 1.0/nfft * numpy.square(magspec(frames, nfft)) def logpowspec(frames, nfft, norm=1): ''' Compute the log power spectrum of each frame in frames. If frames is an NxD matrix, output will be NxNFFT. Args: frames: the array of frames. Each row is a frame. nfft: the FFT length to use. If NFFT > frame_len, the frames are zero-padded. norm: If norm=1, the log power spectrum is normalised so that the max value (across all frames) is 1. Returns: If frames is an NxD matrix, output will be NxNFFT. Each row will be the log power spectrum of the corresponding frame. ''' ps = powspec(frames, nfft) ps[ps <= 1e-30] = 1e-30 lps = 10*numpy.log10(ps) if norm: return lps - numpy.max(lps) else: return lps def preemphasis(signal, coeff=0.95): ''' perform preemphasis on the input signal. Args: signal: The signal to filter. coeff: The preemphasis coefficient. 0 is no filter, default is 0.95. Returns: the filtered signal. ''' return numpy.append(signal[0], signal[1:]-coeff*signal[:-1])