# [SciPy-User] Very simple IIR filters?

Sturla Molden sturla@molden...
Wed Oct 31 09:42:59 CDT 2012

```On 30.10.2012 18:24, Ralf Gommers wrote:

>
> Sorry for being dense, but I'm still not completely clear about what
> you're planning to do now. I think I should read the above as "no Cython
> code". Which sounds good to me.

The code is very simple, though it will also need analog filter design,
error checking, proper documentation, and tests.

Sturla

import numpy as np

def RC(Wn, btype='low'):
""" digital equivalent of an RC circuit """
f = Wn/2.0
x = exp(-2*np.pi*f)
if btype == 'low':
b,a = np.zeros(2),np.zeros(2)
b[0] = 1.0 - x
b[1] = 0.0
a[0] = 1.0
a[1] = - x
elif btype = 'high':
b,a = np.zeros(2),np.zeros(2)
b[0] = (1.0+x)/2.0
b[1] = -(1.0+x)/2.0
a[0] = 1.0
a[1] = - x
else:
raise ValueError, "btype must be 'low' or 'high'"
return b,a

def notch(Wn, bandwidth):
"""
Notch filter to kill line-noise.
"""
f = Wn/2.0
R = 1.0 - 3.0*(bandwidth/2.0)
K = ((1.0 - 2.0*R*np.cos(2*np.pi*f) + R**2)/(2.0 -
2.0*np.cos(2*np.pi*f)))
b,a = np.zeros(3),np.zeros(3)
a[0] = 1.0
a[1] = - 2.0*R*np.cos(2*np.pi*f)
a[2] = R**2
b[0] = K
b[1] = -2*K*np.cos(2*np.pi*f)
b[2] = K
return b,a

def narrowband(Wn, bandwidth):
"""
Narrow-band filter to isolate a single frequency.
"""
f = Wn/2.0
R = 1.0 - 3.0*(bandwidth/2.0)
K = ((1.0 - 2.0*R*np.cos(2*np.pi*f) + R**2)/(2.0 -
2.0*np.cos(2*np.pi*f)))
b,a = np.zeros(3),np.zeros(3)
a[0] = 1.0
a[1] = - 2.0*R*np.cos(2*np.pi*f)
a[2] = R**2
b[0] = 1.0 - K
b[1] = 2.0*(K-R)*np.cos(2*np.pi*f)
b[2] = R**2 - K
return b,a

```