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梅尔倒谱系数(MFCC)实现

2019年07月19日  | 移动技术网IT编程  | 我要评论

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本文实例为大家分享了梅尔倒谱系数实现代码,供大家参考,具体内容如下

""" 
@author: zoutai
@file: mymfcc.py 
@time: 2018/03/26 
@description:
"""
from matplotlib.colors import boundarynorm
import librosa
import librosa.display
import numpy
import scipy.io.wavfile
from scipy.fftpack import dct
import matplotlib.pyplot as plt
import numpy as np


# 第一步-读取音频,画出时域图(采样率-幅度)
sample_rate, signal = scipy.io.wavfile.read('osr_us_000_0010_8k.wav') # file assumed to be in the same directory
signal = signal[0:int(3.5 * sample_rate)]
# plot the wave
time = np.arange(0,len(signal))*(1.0 / sample_rate)
# plt.plot(time,signal)
plt.xlabel("time(s)")
plt.ylabel("amplitude")
plt.title("signal in the time domain ")
plt.grid('on')#标尺,on:有,off:无。


# 第二步-预加重
# 消除高频信号。因为高频信号往往都是相似的,
# 通过前后时间相减,就可以近乎抹去高频信号,留下低频信号。
# 原理:y(t)=x(t)−αx(t−1)

pre_emphasis = 0.97
emphasized_signal = numpy.append(signal[0], signal[1:] - pre_emphasis * signal[:-1])


time = np.arange(0,len(emphasized_signal))*(1.0 / sample_rate)
# plt.plot(time,emphasized_signal)
# plt.xlabel("time(s)")
# plt.ylabel("amplitude")
# plt.title("signal in the time domain after pre-emphasis")
# plt.grid('on')#标尺,on:有,off:无。


# 第三步、取帧,用帧表示
frame_size = 0.025 # 帧长
frame_stride = 0.01 # 步长

# frame_length-一帧对应的采样数, frame_step-一个步长对应的采样数
frame_length, frame_step = frame_size * sample_rate, frame_stride * sample_rate # convert from seconds to samples
signal_length = len(emphasized_signal) # 总的采样数

frame_length = int(round(frame_length))
frame_step = int(round(frame_step))

# 总帧数
num_frames = int(numpy.ceil(float(numpy.abs(signal_length - frame_length)) / frame_step)) # make sure that we have at least 1 frame

pad_signal_length = num_frames * frame_step + frame_length
z = numpy.zeros((pad_signal_length - signal_length))
pad_signal = numpy.append(emphasized_signal, z) # pad signal to make sure that all frames have equal number of samples without truncating any samples from the original signal

# construct an array by repeating a(200) the number of times given by reps(348).
# 这个写法太妙了。目的:用矩阵来表示帧的次数,348*200,348-总的帧数,200-每一帧的采样数
# 第一帧采样为0、1、2...200;第二帧为80、81、81...280..依次类推
indices = numpy.tile(numpy.arange(0, frame_length), (num_frames, 1)) + numpy.tile(numpy.arange(0, num_frames * frame_step, frame_step), (frame_length, 1)).t
frames = pad_signal[indices.astype(numpy.int32, copy=false)] # copy of the array indices
# frame:348*200,横坐标348为帧数,即时间;纵坐标200为一帧的200毫秒时间,内部数值代表信号幅度

# plt.matshow(frames, cmap='hot')
# plt.colorbar()
# plt.figure()
# plt.pcolormesh(frames)


# 第四步、加汉明窗
# 傅里叶变换默认操作的时间段内前后端点是连续的,即整个时间段刚好是一个周期,
# 但是,显示却不是这样的。所以,当这种情况出现时,仍然采用fft操作时,
# 就会将单一频率周期信号认作成多个不同的频率信号的叠加,而不是原始频率,这样就差生了频谱泄漏问题

frames *= numpy.hamming(frame_length) # 相乘,和卷积类似
# # frames *= 0.54 - 0.46 * numpy.cos((2 * numpy.pi * n) / (frame_length - 1)) # explicit implementation **

# plt.pcolormesh(frames)


# 第五步-傅里叶变换频谱和能量谱

# _raw_fft扫窗重叠,将348*200,扩展成348*512
nfft = 512
mag_frames = numpy.absolute(numpy.fft.rfft(frames, nfft)) # magnitude of the fft
pow_frames = ((1.0 / nfft) * ((mag_frames) ** 2)) # power spectrum


# plt.pcolormesh(mag_frames)
#
# plt.pcolormesh(pow_frames)


# 第六步,filter banks滤波器组
# 公式:m=2595*log10(1+f/700);f=700(10^(m/2595)−1)
nfilt = 40 #窗的数目
low_freq_mel = 0
high_freq_mel = (2595 * numpy.log10(1 + (sample_rate / 2) / 700)) # convert hz to mel
mel_points = numpy.linspace(low_freq_mel, high_freq_mel, nfilt + 2) # equally spaced in mel scale
hz_points = (700 * (10**(mel_points / 2595) - 1)) # convert mel to hz
bin = numpy.floor((nfft + 1) * hz_points / sample_rate)

fbank = numpy.zeros((nfilt, int(numpy.floor(nfft / 2 + 1))))
for m in range(1, nfilt + 1):
 f_m_minus = int(bin[m - 1]) # left
 f_m = int(bin[m])  # center
 f_m_plus = int(bin[m + 1]) # right

 for k in range(f_m_minus, f_m):
 fbank[m - 1, k] = (k - bin[m - 1]) / (bin[m] - bin[m - 1])
 for k in range(f_m, f_m_plus):
 fbank[m - 1, k] = (bin[m + 1] - k) / (bin[m + 1] - bin[m])
filter_banks = numpy.dot(pow_frames, fbank.t)
filter_banks = numpy.where(filter_banks == 0, numpy.finfo(float).eps, filter_banks) # numerical stability
filter_banks = 20 * numpy.log10(filter_banks) # db;348*26

# plt.subplot(111)
# plt.pcolormesh(filter_banks.t)
# plt.grid('on')
# plt.ylabel('frequency [hz]')
# plt.xlabel('time [sec]')
# plt.show()


#
# 第七步,梅尔频谱倒谱系数-mfccs
num_ceps = 12 #取12个系数
cep_lifter=22 #倒谱的升个数??
mfcc = dct(filter_banks, type=2, axis=1, norm='ortho')[:, 1 : (num_ceps + 1)] # keep 2-13
(nframes, ncoeff) = mfcc.shape
n = numpy.arange(ncoeff)
lift = 1 + (cep_lifter / 2) * numpy.sin(numpy.pi * n / cep_lifter)
mfcc *= lift #*

# plt.pcolormesh(mfcc.t)
# plt.ylabel('frequency [hz]')
# plt.xlabel('time [sec]')


# 第八步,均值化优化
# to balance the spectrum and improve the signal-to-noise (snr), we can simply subtract the mean of each coefficient from all frames.

filter_banks -= (numpy.mean(filter_banks, axis=0) + 1e-8)
mfcc -= (numpy.mean(mfcc, axis=0) + 1e-8)

# plt.subplot(111)
# plt.pcolormesh(mfcc.t)
# plt.ylabel('frequency [hz]')
# plt.xlabel('time [sec]')
# plt.show()


# 直接频谱分析
# plot the wave
# plt.specgram(signal,fs = sample_rate, scale_by_freq = true, sides = 'default')
# plt.ylabel('frequency(hz)')
# plt.xlabel('time(s)')
# plt.show()



plt.figure(figsize=(10, 4))
mfccs = librosa.feature.melspectrogram(signal,sr=8000,n_fft=512,n_mels=40)
librosa.display.specshow(mfccs, x_axis='time')
plt.colorbar()
plt.title('mfcc')
plt.tight_layout()
plt.show()

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