Matched filter

Signal corrupted with AWGN

from pylab import show

import numpy as np

import matplotlib.pyplot as plt

fs = 4096           # sampling rate [Hz]  

T = 4               # duration [s]

amp = 0.1           # amplitude of the sinusoid 

ome = 13            # frequency of the signal 

N = T*fs            # total number of points 

# time interval spaced with 1/fs 

t = np.arange(0, T, 1./fs)

# white noise 

noise = np.random.normal(size=t.shape)

# sinusoidal signal with amplitude amp

template = amp*np.sin(ome*2*np.pi*t)

# data: signal (template) with added noise 

data = template + noise

plt.figure()

plt.plot(t, data, '-', color="grey")

plt.plot(t, template, '-', color="white", linewidth=2)

plt.xlim(0, T)

plt.xlabel('time')

plt.ylabel('data = signal + noise')

show()

Matched Filter

from numpy import ones,convolve as convol

from matplotlib.pyplot import plot,xlabel,ylabel,title,show

#Matched Filter Output

T =4#

a =2#

t = range(0,T+1)

g = [2*xx for xx in ones([1,T+1])][0]

h  =[abs(x) for x in (convol(g,g))]

for i in range(0,len(h)):

  if(h[i]<0.01):

    h[i]=0

h = [hh-T for hh in h]

t1 = range(0,len(h))

plot(t,g)

xlabel('t--->')

ylabel('g(t)---->')

title('Rectangular pulse duration T = 4, a =2')

show()

plot(t1,h)

xlabel('t--->')

ylabel('Matched Filter output')

title('Output of filter matched to rectangular pulse g(t)')

show()