Implementation of the 3-Base Periodicity Property: https://en.wikipedia.org/wiki/3-Base_Periodicity_Property

3per.py

import matplotlib.pyplot as plt
from numpy.fft import fft
from numpy.fft import fftshift
import numpy as np
import random

dictionary = ['A','C','G','T']

def generate_random_sequence(N):
	return [dictionary[random.randint(0,len(dictionary)-1)] for _ in range(N)]

def char_to_num_seq(s):
	N = len(s)
	u_a, u_c, u_g, u_t = np.zeros(N), np.zeros(N), np.zeros(N), np.zeros(N)
	for i in range(len(s)):
    if s[i] == 'A':
        u_a[i] = 1
    elif s[i] == 'C':
        u_c[i] = 1
    elif s[i] == 'G':
        u_g[i] = 1
    elif s[i] == 'T':
        u_t[i] = 1
	return u_a, u_c, u_g, u_t

def dft(x):
	N = x.shape[0]
	return np.linspace(-np.pi, np.pi, N), fftshift(fft(x))

rand_seq = generate_random_sequence(300)
u_a, u_c, u_g, u_t = char_to_num_seq(rand_seq)
print reduce(lambda a,b: a+b, rand_seq)[:50]

plt.stem(u_a[:50])
plt.show()
plt.stem(u_c[:50])
plt.show()
plt.stem(u_g[:50])
plt.show()
plt.stem(u_t[:50])
plt.show()

u_a -= np.mean(u_a)
u_c -= np.mean(u_c)
u_g -= np.mean(u_g)
u_t -= np.mean(u_t)
f, U_a = dft(u_a)
f, U_c = dft(u_c)
f, U_g = dft(u_t)
f, U_t = dft(u_t)

S = np.abs(U_a)**2 + np.abs(U_c)**2 + np.abs(U_g)**2 + np.abs(U_t)**2
plt.plot(f, S)
print "power at N/3", S[int(N*1.0/2+N*1.0/6)]
print "average power", np.sum(S)/N