Correlation With Python

import array as ar
import matplotlib.pyplot as plt
import math as ma
import random as rn

n = 1000
tmax = 1
dt = tmax/(n-1)
t = ar.array("d",n*[0])
for i in range(n):t[i] = (i-1)*dt
corr = ar.array("d",n*[0])
y = ar.array("d",n*[0])
fr = ar.array("i",n*[0])

A1 = 1.
A2 = 2.
A3 = 1.5
f1 = 4.
f2 = 8.
f3 = 10.
#3 signals andsone noise
for i in range(n):
        y[i] = A1*ma.sin(2.*ma.pi*f1*t[i])
        y[i] = y[i] + A2*ma.sin(2*ma.pi*f2*t[i])
        y[i] = y[i] + A3*ma.sin(2*ma.pi*f3*t[i])
        y[i] = y[i] + rn.random() *10

nfreqs = 10
for f in range(nfreqs):
        fr[f] = f+1
        s = 0
        w = 2*ma.pi*fr[f]/n #divide the argument into n peces
        for j in range(n):s = s + y[j]*ma.sin(w*j)
        corr[f] = 2.*abs(s)/n

print("Frequency \tCorrelation")
for i in range(nfreqs):
        print("%2d \t\t%.5f" %(fr[i],corr[i]))

[fig, p] = plt.subplots(2,1)
p[0].plot(t,y,color='k')
p[0].grid(which='major', color='k',linestyle='--', linewidth=.4)
p[1].vlines(fr,0,corr,colors = 'k')
p[1].grid(which='major', color='k',linestyle='--', linewidth=.4)
plt.show()

Frequency     Correlation
 1         0.10326
 2         0.08844
 3         0.00683
 4         0.99624
 5         0.11656
 6         0.22281
 7         0.09948
 8         2.09447
 9         0.12480
10         1.55338

import array as ar
import matplotlib.pyplot as plt
import math as ma
import random as rn


n = 10000
f1 = 10.5  #false echo frequency
f2 = 10     #echo frequency
ncor =1000
threshold = 480
v = 1.5  # speed of sound in water km/s
corr = ar.array("d",n*[0])
y = ar.array("d",n*[0])
detect = ar.array("d",n*[0])
distance = ar.array("d",n*[0])
tmax = 10
dt = tmax/(n-1)
t = ar.array("d",n*[0])
for i in range(n):t[i] = (i-1)*dt

tsum1 = 0
tsum2 = 0
for i in range(n):
    #false echo
    if t[i] > 2 and t[i] < 3:
        y[i] = ma.sin(2*ma.pi*f1*tsum1)
        tsum1 += dt
     #echo
    if t[i] > 6 and t[i] < 7:
        y[i] = ma.sin(2*ma.pi*f2*tsum2)
        tsum2 += dt
    y[i] += rn.random()
    distance[i] = t[i]*v

w = 2*ma.pi*f2/ncor
for i in range(n-ncor):
        s = 0
        for j in range(ncor):s = s + y[j+i]*ma.sin(w*j)
        corr[i] = abs(s)
        if corr[i] > threshold: detect[i] = 1
        
[fig, p] = plt.subplots(3,1)
p[0].plot(t,y,color='k')
p[0].grid(which='major', color='k',linestyle='--', linewidth=.4)
p[1].vlines(t,0,corr,colors = 'k')
p[1].grid(which='major', color='k',linestyle='--', linewidth=.4)
p[2].vlines(distance,0,detect,colors = 'k')
p[2].grid(which='major', color='k',linestyle='--', linewidth=.4)
p[2].set_xlabel("Target Range Kilometers")
plt.show()

import matplotlib.pyplot as plt
import math
import numpy as np
import random

n = 10_000_000 # Takes about 33s to run on my machine.
nfreqs = 10
tmax = 1


def gen_signal(t):
    A1 = 1.0
    A2 = 2.0
    A3 = 1.5
    f1 = 4.0
    f2 = 8.0
    f3 = 10.0

    y = A1 * math.sin(math.tau * f1 * t)
    y = y + A2 * math.sin(math.tau * f2 * t)
    y = y + A3 * math.sin(math.tau * f3 * t)
    y = y + random.random() * 10
    return y


t = np.arange(0, n) / (n - 1)
y = np.vectorize(gen_signal)(t)
k = np.arange(0, n)
fr = range(1, nfreqs + 1)


def correlate(f, y):
    w = math.tau * f / n
    x = np.vectorize(lambda j: math.sin(w * j))(k)
    return 2.0 * abs(np.sum(y * x)) / n


corr = [correlate(f, y) for f in fr]

print("Frequency \tCorrelation")
for f, c in zip(fr, corr):
    print("%2d \t\t%.5f" % (f, c))