PPT - FIR Filters Design | Signals and Systems - Electronics and Communication Engineering (ECE) PDF Download

 Page 1


AGC
DSP
AGC
DSP
Professor A G Constantinides
15
FIR Design FIR Design
FIR Digital Filter Design FIR Digital Filter Design
Three commonly used approaches to
FIR filter design -
(1) Windowed Fourier series approach
(2) Frequency sampling approach
(3) Computer-based optimization
methods
Page 2


AGC
DSP
AGC
DSP
Professor A G Constantinides
15
FIR Design FIR Design
FIR Digital Filter Design FIR Digital Filter Design
Three commonly used approaches to
FIR filter design -
(1) Windowed Fourier series approach
(2) Frequency sampling approach
(3) Computer-based optimization
methods
AGC
DSP
AGC
DSP
Professor A G Constantinides
16
Finite Impulse Response Finite Impulse Response
Filters Filters
n The transfer function is given by
n The length of Impulse Response is N
n All poles are at           .
n Zeros can be placed anywhere on the z-
plane
å
=
-
=
-
1
0
). ( ) (
N
n
n
z n h z H
0 = z
Page 3


AGC
DSP
AGC
DSP
Professor A G Constantinides
15
FIR Design FIR Design
FIR Digital Filter Design FIR Digital Filter Design
Three commonly used approaches to
FIR filter design -
(1) Windowed Fourier series approach
(2) Frequency sampling approach
(3) Computer-based optimization
methods
AGC
DSP
AGC
DSP
Professor A G Constantinides
16
Finite Impulse Response Finite Impulse Response
Filters Filters
n The transfer function is given by
n The length of Impulse Response is N
n All poles are at           .
n Zeros can be placed anywhere on the z-
plane
å
=
-
=
-
1
0
). ( ) (
N
n
n
z n h z H
0 = z
AGC
DSP
AGC
DSP
Professor A G Constantinides
17
FIR: Linear phase FIR: Linear phase
For phase linearity the FIR transfer
functionmust have zeros outside
the unit circle
Page 4


AGC
DSP
AGC
DSP
Professor A G Constantinides
15
FIR Design FIR Design
FIR Digital Filter Design FIR Digital Filter Design
Three commonly used approaches to
FIR filter design -
(1) Windowed Fourier series approach
(2) Frequency sampling approach
(3) Computer-based optimization
methods
AGC
DSP
AGC
DSP
Professor A G Constantinides
16
Finite Impulse Response Finite Impulse Response
Filters Filters
n The transfer function is given by
n The length of Impulse Response is N
n All poles are at           .
n Zeros can be placed anywhere on the z-
plane
å
=
-
=
-
1
0
). ( ) (
N
n
n
z n h z H
0 = z
AGC
DSP
AGC
DSP
Professor A G Constantinides
17
FIR: Linear phase FIR: Linear phase
For phase linearity the FIR transfer
functionmust have zeros outside
the unit circle
AGC
DSP
AGC
DSP
Professor A G Constantinides
18
FIR: Linear phase FIR: Linear phase
n To develop expression for phase
response set transfer function (order n)
n In factored form
n Where                               ,          is
real & zeros occur in conjugates
n
n
z h z h z h h z H
- - -
+ + + + = ... ) (
2
2
1
1 0
) 1 ( ). 1 ( ) (
1
2
1
1
1
1
-
=
-
=
Õ
-
Õ
- = z z K z H
i
n
i
i
n
i
b a
1 , 1 > <
i i
b a
K
Page 5


AGC
DSP
AGC
DSP
Professor A G Constantinides
15
FIR Design FIR Design
FIR Digital Filter Design FIR Digital Filter Design
Three commonly used approaches to
FIR filter design -
(1) Windowed Fourier series approach
(2) Frequency sampling approach
(3) Computer-based optimization
methods
AGC
DSP
AGC
DSP
Professor A G Constantinides
16
Finite Impulse Response Finite Impulse Response
Filters Filters
n The transfer function is given by
n The length of Impulse Response is N
n All poles are at           .
n Zeros can be placed anywhere on the z-
plane
å
=
-
=
-
1
0
). ( ) (
N
n
n
z n h z H
0 = z
AGC
DSP
AGC
DSP
Professor A G Constantinides
17
FIR: Linear phase FIR: Linear phase
For phase linearity the FIR transfer
functionmust have zeros outside
the unit circle
AGC
DSP
AGC
DSP
Professor A G Constantinides
18
FIR: Linear phase FIR: Linear phase
n To develop expression for phase
response set transfer function (order n)
n In factored form
n Where                               ,          is
real & zeros occur in conjugates
n
n
z h z h z h h z H
- - -
+ + + + = ... ) (
2
2
1
1 0
) 1 ( ). 1 ( ) (
1
2
1
1
1
1
-
=
-
=
Õ
-
Õ
- = z z K z H
i
n
i
i
n
i
b a
1 , 1 > <
i i
b a
K
AGC
DSP
AGC
DSP
Professor A G Constantinides
19
FIR: Linear phase FIR: Linear phase
n Let
where
n Thus
) ( ) ( ) (
2 1
z N z KN z H =
) 1 ln( ) 1 ln( ) ln( )) ( ln(
2
1
1
1
1
1
å
- +
å
- + =
=
-
=
-
n
i
i
n
i
i
z z K z H b a
) 1 ( ) (
1
1
1
1
-
=
Õ
- = z z N
i
n
i
a ) 1 ( ) (
1
2
1
2
-
=
Õ
- = z z N
i
n
i
b