# -*- coding: utf-8 -*- """ Created on Tue Apr 5 22:05:38 2022 @author: Eidos """ # This file includes routines for basic signal processing including framing and computing power spectra. # Author: James Lyons 2012 import decimal import numpy import math import logging def round_half_up(number): return int(decimal.Decimal(number).quantize(decimal.Decimal('1'), rounding=decimal.ROUND_HALF_UP)) def rolling_window(a, window, step=1): # http://ellisvalentiner.com/post/2017-03-21-np-strides-trick shape = a.shape[:-1] + (a.shape[-1] - window + 1, window) strides = a.strides + (a.strides[-1],) return numpy.lib.stride_tricks.as_strided(a, shape=shape, strides=strides)[::step] def framesig(sig, frame_len, frame_step, winfunc=lambda x: numpy.ones((x,)), stride_trick=True): """Frame a signal into overlapping frames. :param sig: the audio signal to frame. :param frame_len: length of each frame measured in samples. :param frame_step: number of samples after the start of the previous frame that the next frame should begin. :param winfunc: the analysis window to apply to each frame. By default no window is applied. :param stride_trick: use stride trick to compute the rolling window and window multiplication faster :returns: an array of frames. Size is NUMFRAMES by frame_len. """ # print('frame_len = ', frame_len) slen = len(sig) frame_len = int(round_half_up(frame_len)) # print('frame_len = ', frame_len) frame_step = int(round_half_up(frame_step)) # print('frame_step = ', frame_step) if slen <= frame_len: numframes = 1 else: numframes = 1 + int(math.ceil((1.0 * slen - frame_len) / frame_step)) # print('numframes = ', numframes) padlen = int((numframes - 1) * frame_step + frame_len) # print('padlen = ', padlen) zeros = numpy.zeros((padlen - slen,)) padsignal = numpy.concatenate((sig, zeros)) # print('padsignal = ', padsignal.size) # print('padsignal = ', padsignal) if stride_trick: win = winfunc(frame_len) frames = rolling_window(padsignal, window=frame_len, step=frame_step) else: 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. :param frames: the array of frames. :param siglen: the length of the desired signal, use 0 if unknown. Output will be truncated to siglen samples. :param frame_len: length of each frame measured in samples. :param frame_step: number of samples after the start of the previous frame that the next frame should begin. :param winfunc: the analysis window to apply to each frame. By default no window is applied. :returns: a 1-D signal. """ frame_len = round_half_up(frame_len) frame_step = round_half_up(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): window_correction[indices[i, :]] = window_correction[ indices[i, :]] + win + 1e-15 # add a little bit so it is never zero 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 Nx(NFFT/2+1). :param frames: the array of frames. Each row is a frame. :param 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 Nx(NFFT/2+1). Each row will be the magnitude spectrum of the corresponding frame. """ if numpy.shape(frames)[1] > NFFT: logging.warn( 'frame length (%d) is greater than FFT size (%d), frame will be truncated. Increase NFFT to avoid.', numpy.shape(frames)[1], NFFT) # print('magspec frames = ', numpy.shape(frames)) # print('magspec frames = ', frames) # print('magspec NFFT = ', numpy.shape(NFFT)) # print('magspec NFFT = ', NFFT) complex_spec = numpy.absolute(numpy.fft.rfft(frames, NFFT)) # print('magspec = ', numpy.shape(complex_spec)) # print('magspec = ', complex_spec) return complex_spec def powspec(frames, NFFT): """Compute the power spectrum of each frame in frames. If frames is an NxD matrix, output will be Nx(NFFT/2+1). :param frames: the array of frames. Each row is a frame. :param 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 Nx(NFFT/2+1). 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 Nx(NFFT/2+1). :param frames: the array of frames. Each row is a frame. :param NFFT: the FFT length to use. If NFFT > frame_len, the frames are zero-padded. :param norm: If norm=1, the log power spectrum is normalised so that the max value (across all frames) is 0. :returns: If frames is an NxD matrix, output will be Nx(NFFT/2+1). 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. :param signal: The signal to filter. :param 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])