Fourier Transform: first trials. Full article at: http://www.firsttimeprogrammer.blogspot.com/2015/05/fourier-transform-first-trials.html

fourier_transform.py

import matplotlib.pyplot as plt
import numpy as np
import scipy as sc

plt.style.use("dark_background")

fs = 1000

# Time
t = np.linspace(0,1.5-1/fs,1500)

# Frequencies in the signal
f1 = 85
f2 = 50
f3 = 75

# Signal
x = 5*np.sin(2*np.pi*f1*t-0.5) + 2*np.cos(2*np.pi*f2*t-0.75) + 2.5*np.cos(2*np.pi*f3*t+1.2)

# Take the FFT of the signal
X = sc.fft(x)

# The time domain representation of the signal
# (use 350 to get the picture I got)
def timeDomain(n=len(t)):
    plt.plot(t[:n],x[:n])
    plt.title("Time domain signal representation")
    plt.xlabel("Time")
    plt.grid(True)
    plt.show()

# Plot the magnitude of the signal
def magnitude():
    plt.plot(abs(X))
    plt.xlabel("Bins")
    plt.ylabel("Magnitude")
    plt.grid(True)
    plt.show()

# Plot the frequency domain signal representation
def frequencyDomain():
    freq = np.linspace(0,500,751)
    plt.plot(freq,abs(X)[:751],'r')
    plt.xlabel("Frequency Hz")
    plt.ylabel("Magnitude")
    plt.title("Frequency domain signal representation")
    plt.grid(True)
    plt.show()