The MATLAB implementation of short-term average zero-crossing rateAnother blogIt has already been introduced here. Here mainly introduces the short-term average zero-crossing rate of the signal in the Python environment, and compares whether the simulation results of MATLAB and Python are consistent.

1. Zero Crossing Rate

Concept: Zero Crossing Rate (ZCR) refers to the number of times the voice signal passes through the zero point (from positive to negative or from negative to positive) in each frame. This feature has been widely used in the fields of speech recognition and music information retrieval, and is a key feature in the classification of percussive sounds.

The mathematical formal definition of ZCR is:

zcr=1T−1∑T−1t=1π{stst−1<0} $zcr=\frac{1}{T-1}{\sum }_{t=1}^{T-1}\pi \left\{s_t{s}_{t-1}<0\right\}$
where s is the value of the sampling point, T is the frame length, and the function π{A} is 1 when A is true, otherwise 0.

Features:
(1). Generally speaking, the ZCR of unvoiced sound and environmental noise is greater than the voiced sound (voiced sound);
(2). Because the ZCR of unvoiced sound and environmental noise are similar in size, they cannot be distinguished by ZCR;
(3). In practice, the zero-crossing rate is often combined with short-term energy characteristics for endpoint detection, especially ZCR is used to detect the beginning and end of unvoiced sounds;
(4). Sometimes ZCR can also be used for rough fundamental frequency estimation, but this is very unreliable unless there is a subsequent refinement process.

2. Short-term average zero-crossing rate of speech signals in Python

The specific code is as follows:
The ZCR Python implementation is as follows:

import math
import numpy as np

def ZeroCR(waveData,frameSize,overLap):
    wlen = len(waveData)
    step = frameSize - overLap
    frameNum = math.ceil(wlen/step)
    zcr = np.zeros((frameNum,1))
    for i in range(frameNum):
        curFrame = waveData[np.arange(i*step,min(i*step+frameSize,wlen))]
        #To avoid DC bias, usually we need to perform mean subtraction on each frame
        curFrame = curFrame - np.mean(curFrame) # zero-justified
        zcr[i] = sum(curFrame[0:-1]*curFrame[1::]<=0)
    return zcr

For a given voice file MORSE.wav, the code to calculate ZCR using the above function is as follows:

import math
import wave
import numpy as np
import pylab as pl

fw = wave.open('F:\【1】Audio\wav\MORSE.wav','rb')
params = fw.getparams()
print(params)
nchannels, sampwidth, framerate, nframes = params[:4]
str_data = fw.readframes(nframes)
wave_data = np.fromstring(str_data, dtype=np.int16)
wave_data = wave_data*1.0/(max(abs(wave_data)))#wave amplitude normalization
fw.close()

# calculate Zero Cross Rate
frameSize = 256
overLap = 0
zcr = ZeroCR(wave_data,frameSize,overLap)

time = np.arange(0, len(wave_data)) * (1.0 / framerate)
time2 = np.arange(0, len(zcr)) * (len(wave_data)/len(zcr) / framerate)
pl.subplot(211)
pl.plot(time, wave_data)
pl.ylabel("Amplitude")
pl.subplot(212)
pl.plot(time2, zcr)
pl.ylabel("ZCR")
pl.xlabel("time (seconds)")
pl.show()

Run the above program to get the following figure:

3. Short-term average zero-crossing rate of speech signals in MATLAB

MATLAB specific code in blogger'sAnother blogIt has already been introduced here.

The results achieved are shown in the following figure:

4. Analysis

It can be seen from the results of MATLAB and Python that the short-term average zero-crossing rates of the two are basically the same.