The difference between IIR and FIR filters can also
be seen by looking at the transfer functions and
noting that the IIR transfer function can be expanded
using a geometric series that is infinite:
1 1 2 3
H ( z) 1
1 z z z .
1 z
The FIR filter is already in a finite series form.
1
H ( z) 1 z .
,Most analog filters have an impulse response which
is infinite in duration. IIR filters are generally
designed by emulating an analog prototype filter.
There are two methods for doing this analog filter
emulation:
(1) the matched z-transform or impulse invariant
transform
(2) the bilinear transformation.
In both cases, we are given an analog transfer
function H(s), and we transform this function into a
digital transfer function H(z).
, The Matched z-Transform
In the matched z-transform digital filter design
method we try to “match” the impulse response of
the analog filter with that of the digital filter being
designed.
To match the impulse responses, we take the
inverse Laplace transform of the analog filter
H(s)h(t), then sample the impulse response
h(t)h[n], then take the z-transform of the sampled
impulse response to get the z-transform transfer
function h[n]H(z).
, Analog Prototype Digital Filter
H (s) H (z )
L-1 Z
sample
h(t ) h[n]
Once we have our z-transform transfer function H(z),
we apply the definition of the transfer function to
write our digital filter equations:
Y ( z)
H ( z) .
X ( z)
be seen by looking at the transfer functions and
noting that the IIR transfer function can be expanded
using a geometric series that is infinite:
1 1 2 3
H ( z) 1
1 z z z .
1 z
The FIR filter is already in a finite series form.
1
H ( z) 1 z .
,Most analog filters have an impulse response which
is infinite in duration. IIR filters are generally
designed by emulating an analog prototype filter.
There are two methods for doing this analog filter
emulation:
(1) the matched z-transform or impulse invariant
transform
(2) the bilinear transformation.
In both cases, we are given an analog transfer
function H(s), and we transform this function into a
digital transfer function H(z).
, The Matched z-Transform
In the matched z-transform digital filter design
method we try to “match” the impulse response of
the analog filter with that of the digital filter being
designed.
To match the impulse responses, we take the
inverse Laplace transform of the analog filter
H(s)h(t), then sample the impulse response
h(t)h[n], then take the z-transform of the sampled
impulse response to get the z-transform transfer
function h[n]H(z).
, Analog Prototype Digital Filter
H (s) H (z )
L-1 Z
sample
h(t ) h[n]
Once we have our z-transform transfer function H(z),
we apply the definition of the transfer function to
write our digital filter equations:
Y ( z)
H ( z) .
X ( z)
