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141 lines
6.0 KiB
141 lines
6.0 KiB
# This file includes routines for basic signal processing including framing and computing power spectra.
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# Author: James Lyons 2012
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import decimal
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import numpy
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import math
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import logging
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def round_half_up(number):
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return int(decimal.Decimal(number).quantize(decimal.Decimal('1'), rounding=decimal.ROUND_HALF_UP))
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def rolling_window(a, window, step=1):
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# http://ellisvalentiner.com/post/2017-03-21-np-strides-trick
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shape = a.shape[:-1] + (a.shape[-1] - window + 1, window)
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strides = a.strides + (a.strides[-1],)
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return numpy.lib.stride_tricks.as_strided(a, shape=shape, strides=strides)[::step]
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def framesig(sig, frame_len, frame_step, winfunc=lambda x: numpy.ones((x,)), stride_trick=True):
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"""Frame a signal into overlapping frames.
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:param sig: the audio signal to frame.
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:param frame_len: length of each frame measured in samples.
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:param frame_step: number of samples after the start of the previous frame that the next frame should begin.
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:param winfunc: the analysis window to apply to each frame. By default no window is applied.
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:param stride_trick: use stride trick to compute the rolling window and window multiplication faster
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:returns: an array of frames. Size is NUMFRAMES by frame_len.
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"""
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slen = len(sig)
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frame_len = int(round_half_up(frame_len))
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frame_step = int(round_half_up(frame_step))
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if slen <= frame_len:
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numframes = 1
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else:
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numframes = 1 + int(math.ceil((1.0 * slen - frame_len) / frame_step))
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padlen = int((numframes - 1) * frame_step + frame_len)
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zeros = numpy.zeros((padlen - slen,))
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padsignal = numpy.concatenate((sig, zeros))
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if stride_trick:
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win = winfunc(frame_len)
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frames = rolling_window(padsignal, window=frame_len, step=frame_step)
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else:
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indices = numpy.tile(numpy.arange(0, frame_len), (numframes, 1)) + numpy.tile(
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numpy.arange(0, numframes * frame_step, frame_step), (frame_len, 1)).T
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indices = numpy.array(indices, dtype=numpy.int32)
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frames = padsignal[indices]
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win = numpy.tile(winfunc(frame_len), (numframes, 1))
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return frames * win
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def deframesig(frames, siglen, frame_len, frame_step, winfunc=lambda x: numpy.ones((x,))):
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"""Does overlap-add procedure to undo the action of framesig.
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:param frames: the array of frames.
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:param siglen: the length of the desired signal, use 0 if unknown. Output will be truncated to siglen samples.
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:param frame_len: length of each frame measured in samples.
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:param frame_step: number of samples after the start of the previous frame that the next frame should begin.
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:param winfunc: the analysis window to apply to each frame. By default no window is applied.
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:returns: a 1-D signal.
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"""
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frame_len = round_half_up(frame_len)
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frame_step = round_half_up(frame_step)
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numframes = numpy.shape(frames)[0]
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assert numpy.shape(frames)[1] == frame_len, '"frames" matrix is wrong size, 2nd dim is not equal to frame_len'
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indices = numpy.tile(numpy.arange(0, frame_len), (numframes, 1)) + numpy.tile(
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numpy.arange(0, numframes * frame_step, frame_step), (frame_len, 1)).T
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indices = numpy.array(indices, dtype=numpy.int32)
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padlen = (numframes - 1) * frame_step + frame_len
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if siglen <= 0: siglen = padlen
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rec_signal = numpy.zeros((padlen,))
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window_correction = numpy.zeros((padlen,))
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win = winfunc(frame_len)
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for i in range(0, numframes):
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window_correction[indices[i, :]] = window_correction[
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indices[i, :]] + win + 1e-15 # add a little bit so it is never zero
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rec_signal[indices[i, :]] = rec_signal[indices[i, :]] + frames[i, :]
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rec_signal = rec_signal / window_correction
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return rec_signal[0:siglen]
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def magspec(frames, NFFT):
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"""Compute the magnitude spectrum of each frame in frames. If frames is an NxD matrix, output will be Nx(NFFT/2+1).
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:param frames: the array of frames. Each row is a frame.
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:param NFFT: the FFT length to use. If NFFT > frame_len, the frames are zero-padded.
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: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.
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"""
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if numpy.shape(frames)[1] > NFFT:
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logging.warn(
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'frame length (%d) is greater than FFT size (%d), frame will be truncated. Increase NFFT to avoid.',
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numpy.shape(frames)[1], NFFT)
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complex_spec = numpy.fft.rfft(frames, NFFT)
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return numpy.absolute(complex_spec)
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def powspec(frames, NFFT):
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"""Compute the power spectrum of each frame in frames. If frames is an NxD matrix, output will be Nx(NFFT/2+1).
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:param frames: the array of frames. Each row is a frame.
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:param NFFT: the FFT length to use. If NFFT > frame_len, the frames are zero-padded.
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: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.
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"""
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return 1.0 / NFFT * numpy.square(magspec(frames, NFFT))
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def logpowspec(frames, NFFT, norm=1):
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"""Compute the log power spectrum of each frame in frames. If frames is an NxD matrix, output will be Nx(NFFT/2+1).
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:param frames: the array of frames. Each row is a frame.
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:param NFFT: the FFT length to use. If NFFT > frame_len, the frames are zero-padded.
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:param norm: If norm=1, the log power spectrum is normalised so that the max value (across all frames) is 0.
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: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.
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"""
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ps = powspec(frames, NFFT);
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ps[ps <= 1e-30] = 1e-30
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lps = 10 * numpy.log10(ps)
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if norm:
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return lps - numpy.max(lps)
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else:
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return lps
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def preemphasis(signal, coeff=0.95):
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"""perform preemphasis on the input signal.
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:param signal: The signal to filter.
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:param coeff: The preemphasis coefficient. 0 is no filter, default is 0.95.
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:returns: the filtered signal.
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"""
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return numpy.append(signal[0], signal[1:] - coeff * signal[:-1])
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