Design of Digital filter using Digital to
Digital transformation
There exists a set
of transformation that takes a low pass digital
filter and turn into highpass, bandpass, bandstop
or another lowpass digital filter. These transformations
are given in table 9.1.
The transformations
all take the form of replacing the in by
some
function of.
Type From
To
Transformation
Design Formula
Low pass cutoff
Low pass cutoff
LPF
HPF
LPF
BPF
LPF
BSF
Starting with a set
of digital specifications and using the inverse
of the design equation given in table 9.1, a
set of lowpass digital requirements can be established.
A LPF digital prototype filter is
then selected to satisfy these requirements and
the proper digital to digital transformation
is applied to give the desired.
Example
Using the digital
to digital transformation, find the system function for
a low-pass digital filter that satisfies the
following set the requirements (a) monotone stop
and passband (b)-3dB cutoff frequency of (c)
attenuation at and past is
at least 15dB.
Because of monotone requirement, a Butterworth
filter is selected. The required n is given by
rounded to 2.
For we
get from table 9.1. ,
From standard tables (or MATLAB) we find standard
2 nd order Butterworth filter with cut
off and
then apply the digital transform to get
in 
by
some
function of. 
is
then selected to satisfy these requirements and
the proper digital to digital transformation
is applied to give the desired. 
for
a low-pass digital filter that satisfies the
following set the requirements (a) monotone stop
and passband (b)-3dB cutoff frequency of 
(c)
attenuation at and past 
is
at least 15dB. 
we
get from table 9.1. 
,
From standard tables (or MATLAB) we find standard
2 nd order Butterworth filter with cut
off 
and
then apply the digital transform to get 
