# calculate filterbank features. Provides e.g. fbank and mfcc features for use in ASR applications
# Author: James Lyons 2012
from __future__ import division
import numpy
from python_kaldi_features import sigproc
from scipy.fftpack import dct

def mfcc(signal,samplerate=16000,winlen=0.025,winstep=0.01,numcep=13,
         nfilt=23,nfft=512,lowfreq=20,highfreq=None,dither=1.0,remove_dc_offset=True,preemph=0.97,
         ceplifter=22,useEnergy=True,wintype='povey'):
    """Compute MFCC features from an audio signal.

    :param signal: the audio signal from which to compute features. Should be an N*1 array
    :param samplerate: the samplerate of the signal we are working with.
    :param winlen: the length of the analysis window in seconds. Default is 0.025s (25 milliseconds)
    :param winstep: the step between successive windows in seconds. Default is 0.01s (10 milliseconds)
    :param numcep: the number of cepstrum to return, default 13
    :param nfilt: the number of filters in the filterbank, default 26.
    :param nfft: the FFT size. Default is 512.
    :param lowfreq: lowest band edge of mel filters. In Hz, default is 0.
    :param highfreq: highest band edge of mel filters. In Hz, default is samplerate/2
    :param preemph: apply preemphasis filter with preemph as coefficient. 0 is no filter. Default is 0.97.
    :param ceplifter: apply a lifter to final cepstral coefficients. 0 is no lifter. Default is 22.
    :param appendEnergy: if this is true, the zeroth cepstral coefficient is replaced with the log of the total frame energy.
    :param winfunc: the analysis window to apply to each frame. By default no window is applied. You can use numpy window functions here e.g. winfunc=numpy.hamming
    :returns: A numpy array of size (NUMFRAMES by numcep) containing features. Each row holds 1 feature vector.
    """
    feat,energy = fbank(signal,samplerate,winlen,winstep,nfilt,nfft,lowfreq,highfreq,dither,remove_dc_offset,preemph,wintype)
    feat = numpy.log(feat)
    feat = dct(feat, type=2, axis=1, norm='ortho')[:,:numcep]
    feat = lifter(feat,ceplifter)
    if useEnergy: feat[:,0] = numpy.log(energy) # replace first cepstral coefficient with log of frame energy
    return feat

def fbank(signal,samplerate=16000,winlen=0.025,winstep=0.01,
          nfilt=40,nfft=512,lowfreq=0,highfreq=None,dither=1.0,remove_dc_offset=True, preemph=0.97, 
          wintype='hamming'):
    """Compute Mel-filterbank energy features from an audio signal.

    :param signal: the audio signal from which to compute features. Should be an N*1 array
    :param samplerate: the samplerate of the signal we are working with.
    :param winlen: the length of the analysis window in seconds. Default is 0.025s (25 milliseconds)
    :param winstep: the step between successive windows in seconds. Default is 0.01s (10 milliseconds)
    :param nfilt: the number of filters in the filterbank, default 26.
    :param nfft: the FFT size. Default is 512.
    :param lowfreq: lowest band edge of mel filters. In Hz, default is 0.
    :param highfreq: highest band edge of mel filters. In Hz, default is samplerate/2
    :param preemph: apply preemphasis filter with preemph as coefficient. 0 is no filter. Default is 0.97.
    :param winfunc: the analysis window to apply to each frame. By default no window is applied. You can use numpy window functions here e.g. winfunc=numpy.hamming
     winfunc=lambda x:numpy.ones((x,))   
    :returns: 2 values. The first is a numpy array of size (NUMFRAMES by nfilt) containing features. Each row holds 1 feature vector. The
        second return value is the energy in each frame (total energy, unwindowed)
    """
    highfreq= highfreq or samplerate/2
    frames,raw_frames = sigproc.framesig(signal, winlen*samplerate, winstep*samplerate, dither, preemph, remove_dc_offset, wintype)
    pspec = sigproc.powspec(frames,nfft) # nearly the same until this part
    energy = numpy.sum(raw_frames**2,1) # this stores the raw energy in each frame
    energy = numpy.where(energy == 0,numpy.finfo(float).eps,energy) # if energy is zero, we get problems with log

    fb = get_filterbanks(nfilt,nfft,samplerate,lowfreq,highfreq)
    feat = numpy.dot(pspec,fb.T) # compute the filterbank energies
    feat = numpy.where(feat == 0,numpy.finfo(float).eps,feat) # if feat is zero, we get problems with log

    return feat,energy

def logfbank(signal,samplerate=16000,winlen=0.025,winstep=0.01,
          nfilt=40,nfft=512,lowfreq=64,highfreq=None,dither=1.0,remove_dc_offset=True,preemph=0.97,wintype='hamming'):
    """Compute log Mel-filterbank energy features from an audio signal.

    :param signal: the audio signal from which to compute features. Should be an N*1 array
    :param samplerate: the samplerate of the signal we are working with.
    :param winlen: the length of the analysis window in seconds. Default is 0.025s (25 milliseconds)
    :param winstep: the step between successive windows in seconds. Default is 0.01s (10 milliseconds)
    :param nfilt: the number of filters in the filterbank, default 26.
    :param nfft: the FFT size. Default is 512.
    :param lowfreq: lowest band edge of mel filters. In Hz, default is 0.
    :param highfreq: highest band edge of mel filters. In Hz, default is samplerate/2
    :param preemph: apply preemphasis filter with preemph as coefficient. 0 is no filter. Default is 0.97.
    :returns: A numpy array of size (NUMFRAMES by nfilt) containing features. Each row holds 1 feature vector.
    """
    feat,energy = fbank(signal,samplerate,winlen,winstep,nfilt,nfft,lowfreq,highfreq,dither, remove_dc_offset,preemph,wintype)
    return numpy.log(feat)

def hz2mel(hz):
    """Convert a value in Hertz to Mels

    :param hz: a value in Hz. This can also be a numpy array, conversion proceeds element-wise.
    :returns: a value in Mels. If an array was passed in, an identical sized array is returned.
    """
    return 1127 * numpy.log(1+hz/700.0)


def mel2hz(mel):
    """Convert a value in Mels to Hertz

    :param mel: a value in Mels. This can also be a numpy array, conversion proceeds element-wise.
    :returns: a value in Hertz. If an array was passed in, an identical sized array is returned.
    """
    return 700 * (numpy.exp(mel/1127.0)-1)

def get_filterbanks(nfilt=26,nfft=512,samplerate=16000,lowfreq=0,highfreq=None):
    """Compute a Mel-filterbank. The filters are stored in the rows, the columns correspond
    to fft bins. The filters are returned as an array of size nfilt * (nfft/2 + 1)

    :param nfilt: the number of filters in the filterbank, default 20.
    :param nfft: the FFT size. Default is 512.
    :param samplerate: the samplerate of the signal we are working with. Affects mel spacing.
    :param lowfreq: lowest band edge of mel filters, default 0 Hz
    :param highfreq: highest band edge of mel filters, default samplerate/2
    :returns: A numpy array of size nfilt * (nfft/2 + 1) containing filterbank. Each row holds 1 filter.
    """
    highfreq= highfreq or samplerate/2
    assert highfreq <= samplerate/2, "highfreq is greater than samplerate/2"

    # compute points evenly spaced in mels
    lowmel = hz2mel(lowfreq)
    highmel = hz2mel(highfreq)

    # check kaldi/src/feat/Mel-computations.h    
    fbank = numpy.zeros([nfilt,nfft//2+1])
    mel_freq_delta = (highmel-lowmel)/(nfilt+1)
    for j in range(0,nfilt):
        leftmel = lowmel+j*mel_freq_delta
        centermel = lowmel+(j+1)*mel_freq_delta
        rightmel = lowmel+(j+2)*mel_freq_delta
        for i in range(0,nfft//2):
            mel=hz2mel(i*samplerate/nfft)
            if mel>leftmel and mel<rightmel:
                if mel<centermel:
                    fbank[j,i]=(mel-leftmel)/(centermel-leftmel)
                else:
                    fbank[j,i]=(rightmel-mel)/(rightmel-centermel)
    return fbank

def lifter(cepstra, L=22):
    """Apply a cepstral lifter the the matrix of cepstra. This has the effect of increasing the
    magnitude of the high frequency DCT coeffs.

    :param cepstra: the matrix of mel-cepstra, will be numframes * numcep in size.
    :param L: the liftering coefficient to use. Default is 22. L <= 0 disables lifter.
    """
    if L > 0:
        nframes,ncoeff = numpy.shape(cepstra)
        n = numpy.arange(ncoeff)
        lift = 1 + (L/2.)*numpy.sin(numpy.pi*n/L)
        return lift*cepstra
    else:
        # values of L <= 0, do nothing
        return cepstra

def delta(feat, N):
    """Compute delta features from a feature vector sequence.

    :param feat: A numpy array of size (NUMFRAMES by number of features) containing features. Each row holds 1 feature vector.
    :param N: For each frame, calculate delta features based on preceding and following N frames
    :returns: A numpy array of size (NUMFRAMES by number of features) containing delta features. Each row holds 1 delta feature vector.
    """
    if N < 1:
        raise ValueError('N must be an integer >= 1')
    NUMFRAMES = len(feat)
    denominator = 2 * sum([i**2 for i in range(1, N+1)])
    delta_feat = numpy.empty_like(feat)
    padded = numpy.pad(feat, ((N, N), (0, 0)), mode='edge')   # padded version of feat
    for t in range(NUMFRAMES):
        delta_feat[t] = numpy.dot(numpy.arange(-N, N+1), padded[t : t+2*N+1]) / denominator   # [t : t+2*N+1] == [(N+t)-N : (N+t)+N+1]
    return delta_feat
