Basic implementation of FIR filter with given coefficients

fir.py

'''
Basic implementation of FIR filter with given coefficients

Y[n] = sum(f(i)*g(n-i))
'''

__author__ = 'Darko Lukic'
__email__ = 'lukicdarkoo@gmail.com'



import numpy as np
import matplotlib.pyplot as plt


SAMPLE_RATE = 8192
N = 128 # Windowing

# Generated with: http://t-filter.engineerjs.com/
filter = [
  38187311164.760864,
  222104632565.16745,
  -278907616677.3709,
  -494639530286.5757,
  617425373598.061,
  255943274597.81885,
  -64755010449.17185,
  -695553688939.9774,
  -271477106814.2853,
  1101809427479.7473,
  292604714803.50635,
  -553556367022.7665,
  -1329404651336.4807,
  637666123638.598,
  1530947087313.8647,
  491084885187.5182,
  -2426202180883.679,
  -2392282493314.974,
  6638011630752.459,
  -2392282493314.974,
  -2426202180883.679,
  491084885187.5182,
  1530947087313.8647,
  637666123638.598,
  -1329404651336.4807,
  -553556367022.7665,
  292604714803.50635,
  1101809427479.7473,
  -271477106814.2853,
  -695553688939.9774,
  -64755010449.17185,
  255943274597.81885,
  617425373598.061,
  -494639530286.5757,
  -278907616677.3709,
  222104632565.16745,
  38187311164.760864
]

# Convolution is used to apply filter
def convolution(input_signal, filter):
	output_signal = list()
	for n in xrange(0, len(input_signal) - len(filter)):
		output_signal.append(0)

		'''
		After few experiments this method gives the best result. I mean on:
		int(np.floor(len(input_signal)/len(filter)))
		'''
		for i in xrange(0, int(np.floor(len(input_signal)/len(filter))) * len(filter)):
			output_signal[n] += filter[i%len(filter)] * input_signal[n-i]

	return output_signal
	

# Make two sine signals frequencies of 128Hz and 256Hz
x_values = np.arange(0, N, 1)
x = np.sin((2*np.pi*x_values / 32.0)) # 32 - 256Hz
x += np.sin((2*np.pi*x_values / 64.0)) # 64 - 128Hz

Y = convolution(x, filter)
#Y = np.convolve(x, filter, 'valid')


# Plotting 
_, plots = plt.subplots(3)

## Plot in time domain
plots[0].plot(x)
plots[1].plot(Y)


## Plot filtered signal in frequent domain
S = np.fft.fft(Y);
powers_all = np.abs(np.divide(S, N/2))
powers = powers_all[0:N/2]
frequencies = np.divide(np.multiply(SAMPLE_RATE, np.arange(0, N/2)), N)
plots[2].plot(frequencies, powers)

plt.show()