 Alex - 3 years ago 409
Python Question

# Filtering signal with Python lfilter

I'm new with Python and I'm completely stuck when filtering a signal. This is the code:

``````import numpy as np
import matplotlib.pyplot as plt
from scipy import signal

fs=105e6
fin=70.1e6

N=np.arange(0,21e3,1)

# Create a input sin signal of 70.1 MHz sampled at 105 MHz
x_in=np.sin(2*np.pi*(fin/fs)*N)

# Define the "b" and "a" polynomials to create a CIC filter (R=8,M=2,N=6)
b=np.zeros(97)
b[[0,16,32,48,64,80,96]]=[1,-6,15,-20,15,-6,1]
a=np.zeros(7)
a[[0,1,2,3,4,5,6]]=[1,-6,15,-20,15,-6,1]

w,h=signal.freqz(b,a)
plt.plot(w/max(w),20*np.log10(abs(h)/np.nanmax(h)))
plt.title('CIC Filter Response')

output_nco_cic=signal.lfilter(b,a,x_in)

plt.figure()
plt.plot(x_in)
plt.title('Input Signal')
plt.figure()
plt.plot(output_nco_cic)
plt.title('Filtered Signal')
``````

And the plots: As you can see, although the filter transfer function is correct, the output isn't. And I can't see why my code isn't working. I've coded the same in Matlab and the output looks ok.

Thaks for the help! Patrick Maupin

I don't find it confusing that this didn't work with Python, but I do find it confusing that it worked with Matlab.

CIC filters don't work with floating point numbers.

UPDATE:

Interestingly, at least with the version of scipy I have, lfilter doesn't work with integer arrays -- I get a NotImplemented error. Here is a numpy version of a CIC filter that is about twice as fast as a pure Python implementation on my machine:

``````# Implements an in-memory CIC decimator using numpy.

from math import log
from numpy import int32, int64, array

def cic_decimator(source, decimation_factor=32, order=5, ibits=1, obits=16):

# Calculate the total number of bits used internally, and the output
numbits = order * int(round(log(decimation_factor) / log(2))) + ibits
outshift = numbits - obits
outmask  = (1 << obits) - 1

# If we need more than 64 bits, we can't do it...
assert numbits <= 64

# Create a numpy array with the source
result = array(source, int64 if numbits > 32 else int32)

# Do the integration stages
for i in range(order):
result.cumsum(out=result)

# Decimate
result = array(result[decimation_factor - 1 : : decimation_factor])

# Do the comb stages.  Iterate backwards through the array,
# because we use each value before we replace it.
for i in range(order):
result[len(result) - 1 : 0 : -1] -= result[len(result) - 2 : : -1]

# Normalize the output
result >>= outshift