这是读取音频文件FFT的正确方法吗？ （python + wav）

Question

The audio file is a 16bit mono PCM audio file with varying samplerates and length of 10-30ms.

import struct
from pydub import AudioSegment
import numpy as np
import matplotlib.pyplot as plt
import scipy.fftpack

sound = AudioSegment.from_wav("3000hz.wav")

raw_data = sound.raw_data# needs to be mono
sample_rate = sound.frame_rate
sample_size = sound.sample_width
channels = sound.channels

fmt = "%ih" % sound.frame_count() * channels
amplitudes= struct.unpack(fmt, raw_data)
yVals = scipy.fftpack.fft(amplitudes)

plt.plot(abs(yVals[:(len(yVals)/2)-1]),'r')
plt.show()

The output with a 3000hz wav file(taken from an online sin wave generator) results in a decent looking FFT but spikes at 9000, not 3000. This off by a factor of 3 is consistent in other tests. Is this ok? And is the code correct?

Answer 1

By calling plt.plot() with only an y array and no corresponding x array, it will use 0, 1, ..., N-1 as the x values. This is not what we actually want, we want the frequency on the x-axis.

Let's denote the x value you see in the plot right now by "bin index". Let the length of the array be N and the sampling frequency be fs . When calculating an FFT, the bin index 0 corresponds to a frequency of 0 Hz. The next bin index 1 corresponds to the frequency fs / N Hz. This is because the FFT will have N values and go from 0 Hz to fs Hz, so each step is fs / N Hz. The next bin thus corresponds to 2 * fs / N Hz, and so on. And the last bin N-1 is (N-1)/N * fs Hz, so almost fs Hz.

If we want to create a plot where you have amplitude spectrum vs. frequency, then we need to manually create a frequency vector which contains the real frequency for each bin index. Luckily, scipy.fftpack contains a function for that: fftfreq :

freq = scipy.fftpack.fftfreq(n=N, d=1.0 / fs)

Then we can modify the call to plt.plot() to use freq as the x values instead of 0 ... N-1 :

plt.plot(freq, abs(yVals), 'r')

With that, the peak should be at the correct position.

If you only want to see a single-sided spectrum, then you can crop both freq and yVals like you already do in the code in the question.