Plotting numpy rfft

Question

I am trying to plot the fft of a wav file, I have successfully completed it using the regular fft but I wanted to experiment with rfft as my application was to perform this in music. When I try to plot xf and yf (figure 2) I run into an issue where xf is half the length of yf and I can't figure out why, I assume its due to the negative frequencies missing but I thought changing both function calls to rfft and rfftfreq would handle it.

import numpy as np
import soundfile as sf
import matplotlib.pyplot as plt

square = 'square.wav'
sine = 'sine.wav'
k = '1Khz.wav'
cello = 'cello.wav'
data, fs = sf.read(k)

#Plot the Signal
N = len(data)
T = 1.0/fs
x = np.linspace(0, (N*T), N)
plt.plot(x, data)
plt.grid()
count = 0

yf = np.fft.rfft(data)
xf = np.fft.rfftfreq(yf.size, d=T)

plt.figure(2)
plt.plot(xf, yf)
plt.show()

SleuthEye · Accepted Answer · 2018-03-11 20:36:52Z

1

The sizes used for numpy.fft.rfft and numpy.fft.rfftfreq need to match. As such you should use your data.size rather yf.size (since the size of yf is already reduced by not including the negative frequencies) as argument to rfftfreq:

yf = np.fft.rfft(data)
xf = np.fft.rfftfreq(data.size, d=T)

Finally note that as you plot yf with plt.plot(xf, yf) you would get a warning about the imaginary part being lost. If you are interested in plotting the magnitude of the frequency spectrum, you should rather use plt.plot(xf, abs(yf)).

answered Mar 11, 2018 at 20:36

SleuthEye

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Joe · Accepted Answer · 2018-03-09 20:12:18Z

0

You need to convert the frequencies to the sample rate. See https://stackoverflow.com/a/27191172/7919597 or the doc of rfftfreq:

signal = np.array([-2, 8, 6, 4, 1, 0, 3, 5, -3, 4], dtype=float)
fourier = np.fft.rfft(signal)
n = signal.size
sample_rate = 100
freq = np.fft.fftfreq(n, d=1./sample_rate)
print(freq)
freq = np.fft.rfftfreq(n, d=1./sample_rate)
print(freq)

answered Mar 9, 2018 at 20:12

Joe

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