komunikilo 0.1.5

A chaotic communications simulator.
Documentation 
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#!/usr/bin/env python3
import matplotlib.pyplot as plt
import numpy as np

plt.style.use('seaborn-poster')

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.figure(figsize = (8, 6))
plt.stem(freq, abs(X), 'b', \
         markerfmt=" ", basefmt="-b")
plt.xlabel('Freq (Hz)')
plt.ylabel('DFT Amplitude |X(freq)|')
plt.show()

def FFT(x):
    """
    A recursive implementation of 
    the 1D Cooley-Tukey FFT, the 
    input should have a length of 
    power of 2. 
    """
    N = len(x)
    
    if N == 1:
        return x
    else:
        X_even = FFT(x[::2])
        X_odd = FFT(x[1::2])
        factor = \
          np.exp(-2j*np.pi*np.arange(N)/ N)
        
        X = np.concatenate(\
            [X_even+factor[:int(N/2)]*X_odd,
             X_even+factor[int(N/2):]*X_odd])
        return X

# sampling rate
sr = 128
# 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.figure(figsize = (8, 6))
plt.plot(t, x, 'r')
plt.ylabel('Amplitude')

plt.show()