1
Transformation of LPF to other filters
c : is the analog frequency
Butterworth Filter:
Filter Order Transfer Function
1
1
1
s
2
12
12 ss
3
122
123 sss
4
1613.24142.36131.2
1234 ssss
Bilinear Transformation:
The analog frequency ( c ) =
2
)(tan
2 frequencydigital
Ts,
1
1
1
12
z
z
Ts
s
2
Properties of Laplace Transform
Property Signal Laplace Transform Time Shifting )( 0ttx )(0 sXe
tS Shift in S-domain )(txe tS o )( 0ssX
Differentiation in the Time
domain )(txdt
d
)(sXs
Differentiation in the s-
domain )(txt
)(sXsd
d
3
4
5
Use the matrix NW to find the DFT using the relation: NNN xWX .
Where
)1)(1()1(21
)1(242
12
....1
........
....1
....1
1....111
NN
N
N
N
N
N
N
NNN
N
NNN
N
www
www
www
W and
Nj
N ew
2
6
