Introduction

Study material for signal processing in Python.

Library to use

numpy, matplotlib scipy fftpack

Execution content

Generate a sine wave of a specific frequency. (numpy)
Run the FFT. (scipy)
Plot the execution result. (matplotlib)

Program code

1. Sine wave generation part

N = 2**20 # data number
dt = 0.0001 # data step [s]
f1 = 5 # frequency[Hz]
A1 = 1 # Amplitude
p1 = 90*pi/180  # phase [rad]

#Waveform formation
t = np.arange(0, N*dt, dt) # time
freq = np.linspace(0, 1.0/dt, N) # frequency step
y = A1*np.sin(2*np.pi*f1*t + p1)

2. Fourier transform part

#Discrete Fourier transform&Standardization
yf = fft(y)/(N/2) 

# y :numpy array
# N :Number of samplings

Whole code

`fft.py`


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

#Pi
pi = np.pi

# parameters

N = 2**20 # data number
dt = 0.0001 # data step [s]
f1 = 5 # frequency[Hz]
A1 = 1 # Amplitude
p1 = 90*pi/180 # phase

#Waveform formation
t = np.arange(0, N*dt, dt) # time
freq = np.linspace(0, 1.0/dt, N) # frequency step

y = A1*np.sin(2*np.pi*f1*t + p1)

#Fourier transform
yf = fft(y)/(N/2) #Discrete Fourier transform&Standardization

#plot
plt.figure(2)

plt.subplot(211)
plt.plot(t, y)
plt.xlim(0, 1)
plt.xlabel("time")
plt.ylabel("amplitude")

plt.subplot(212)
plt.plot(freq, np.abs(yf))
plt.xlim(0, 10)
plt.xlabel("frequency")
plt.ylabel("amplitude")

plt.tight_layout()
plt.savefig("01")

plt.show()

3. Execution result

Top: Time domain graph: Confirm that the phase is 90 degrees out of phase. Bottom: Frequency domain graph: 5Hz frequency confirmed.

Signal processing in Python (1): Fourier transform