FFT sample in Python2.7

fft_paper.pdf

test_fft.py

# build a sample array of discrete value
# compute the FFT and display spectral graphic

from scipy.fftpack import fft
import matplotlib.pyplot as plt
import numpy as np
import random as rd

# number of samples
Ns = 10000

# second between 2 samples
Ts = 0.002 # 2 ms

# N samples, every sample is time value (in s)
# 0 -> t_max with Ns items
t_max = Ns * Ts
t_samples = np.linspace(0.0, t_max, Ns)

# sum of :
#  50 Hz sin  30%
#  80 Hz sin 100%
# 100 Hz sin  50%
# 200 Hz sin 100%
y_samples =   0.3 * np.sin(50.0 * 2.0 * np.pi * t_samples) \
            + 1.0 * np.sin(80.0 * 2.0 * np.pi * t_samples) \
            + 0.5 * np.sin(100.0 * 2.0 * np.pi * t_samples) \
            + 1.0 * np.sin(200.0 * 2.0 * np.pi * t_samples)

# add some noise (Ns sample value between [-1.0 and 1.0])
s_noise = (np.random.rand(Ns)-0.5)*2
y_samples += s_noise

# compute FFT
y_freq = fft(y_samples)

# frequency domain max freq is (1.0/periods), periods
# 0 -> f_max with Ns/2 steps, xf in Hz
f_max = 1.0/(2.0*Ts)
xf = np.linspace(0.0, f_max, Ns/2)

# yf between 0.0 and 1.0 for every xf step
yf = 1.0/(Ns/2.0) * np.abs(y_freq[0:Ns/2])

# build spectral graphic
plt.plot(xf, yf)
plt.grid()
plt.show()