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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
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29 videos|76 docs|63 tests

FAQs on PPT - FIR Filters Design - Signals and Systems - Electronics and Communication Engineering (ECE)

1. What are FIR filters?
Ans. FIR filters, or Finite Impulse Response filters, are a type of digital filter used in signal processing. They have a finite impulse response, meaning that their output depends only on a finite number of input samples.
2. How are FIR filters designed?
Ans. FIR filters are designed by determining the desired frequency response and then applying a mathematical algorithm, such as the windowing method or the frequency sampling method, to calculate the filter coefficients. The coefficients determine the filter's behavior in the frequency domain.
3. What is the advantage of using FIR filters?
Ans. FIR filters have several advantages, including linear phase response, stability, and the ability to achieve a sharp cutoff or desired frequency response. They are also relatively simple to design and implement.
4. Can FIR filters be used for real-time applications?
Ans. Yes, FIR filters can be used for real-time applications. Since they have a finite impulse response, there is no feedback loop involved, making them suitable for real-time processing where latency and stability are important factors.
5. Are there any limitations to using FIR filters?
Ans. While FIR filters have numerous advantages, they also have some limitations. One limitation is that they require a longer filter length compared to other filter types, which can increase the computational requirements. Additionally, FIR filters may not be as efficient in terms of frequency selectivity compared to some other types of filters.
29 videos|76 docs|63 tests
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