4. Properties of an IIR Filter
• The general equation of an IIR filter can be
expressed as follows:
M
k
k
k
N
k
k
k
M
M
N
N
za
zb
zaza
zbzbb
zH
1
0
1
1
1
10
1
1
ak and bk are the filter coefficients.
5. Properties of an IIR Filter
• The transfer function can be factorised to
give:
zX
zY
pzpzpz
zzzzzz
kzH
N
N
21
21
Where: z1, z2, …, zN are the zeros,
p1, p2, …, pN are the poles.
6. Properties of an IIR Filter
• The transfer function can be factorised to
give:
zX
zY
pzpzpz
zzzzzz
kzH
N
N
21
21
For the implementation of the above
equation we need the difference equation:
M
k
k
N
k
k
k
knyaknxb
knxkhny
10
0
7. Advantage
Use less memory than FIR filters
Disadvantages
•They are more susceptable to problems of finite-length arithmetic, such as
noise generated by calculations, and limit cycles. (This is a direct
consequence of feedback: when the output isn't computed perfectly and is
fed back, the imperfection can compound.)
•They are harder (slower) to implement using fixed-point arithmetic.
•They don't offer the computational advantages of FIR filters for multirate
(decimation and interpolation) applications.
20. Reference for this
lecture:
Drijkoningen, G. G. and Verschuur, D.J., 2003. Seismic data processing. TU Delft.
http://geodus1.ta.tudelft.nl/PrivatePages/G.G.Drijkoningen/Lectur
eNotes/SeismicProcessing%28tg001_ta3600%29.pdf
Link