DiscreteFourierTransform.py

#Harshit Miglani
#22/17053
#references:
#https://pythonnumericalmethods.berkeley.edu/notebooks/chapter24.02-Discrete-Fourier-Transform.html
#https://pythonnumericalmethods.berkeley.edu/notebooks/chapter24.00-Fourier-Transforms.html
#PDF's in PDF folder

import matplotlib.pyplot as plt
import numpy as np
# sampling rate
sr = 100
# sampling interval
ts = 1.0/sr
t = np.arange(0,1,ts)

freq = 1.
x = 3*np.sin(2*np.pi*freq*t)

freq = 4
x += np.sin(2*np.pi*freq*t)

freq = 7
x += 0.5* np.sin(2*np.pi*freq*t)

plt.plot(t, x, 'r')
plt.ylabel('Amplitude')

plt.show()


def DFT(x):
    """
    Function to calculate the
    discrete Fourier Transform
    of a 1D real-valued signal x
    """

    N = len(x)
    n = np.arange(N)
    k = n.reshape((N, 1))
    e = np.exp(-2j * np.pi * k * n / N)

    X = np.dot(e, x)

    return X

X = DFT(x)

# calculate the frequency
N = len(X)
n = np.arange(N)
T = N/sr
freq = n/T
plt.stem(freq, abs(X),markerfmt=" ", basefmt="-b")
plt.xlabel('Freq (Hz)')
plt.ylabel('DFT Amplitude')
plt.show()

n_oneside = N//2
# get the one side frequency
f_oneside = freq[:n_oneside]

# normalize the amplitude
X_oneside =X[:n_oneside]/n_oneside

plt.xlabel('Freq (Hz)')
plt.ylabel('DFT Amplitude')
plt.stem(f_oneside, abs(X_oneside), 'b', markerfmt=" ", basefmt="-b")
plt.xlim(-1, 11)
plt.show()