9/10/2024
Introduction to Digital Filter
@
Sardar Patel Institute of
Technology, Andheri, Mumbai
Dr. Kiran TALELE
Bharatiya Vidya Bhavans’
Sardar Patel Institute of Technology Andheri(w) Mumbai
Dr. Kiran TALELE
Teacher . Instructor . Guide . Mentor . Coach
@ Bharatiya Vidya Bhavans’ Sardar Patel Institute of
Technology Andheri(w) Mumbai
• Associate Professor, Electronics Engineering Department (1997)
• Dean, Students, Alumni & External Relations (2022)
@ Sardar Patel Technology Business Incubator(SP-TBI),
Funded by Department of Science & Technology(DST),
Govt. of India
• Co-ordinator (2015)
@ IEEE Bombay Section
• Treasurer (2020)
• Executive Committee Member (2015)
Digital Filters
Kiran.Tulshiram.Vasumati.Talele
9987030881 kiran.talele@spit.ac.in
1
9/10/2024
Digital Filter
H(Z) h(n) DE
RD PZ FR
* DT System *
x[n] y[n]
Ex. Digital Filter
Infinite Impulse Finite Impulse
Response(IIR) Filter Repsonse(FIR) Filter
Ex. h[n] = (0.5)n u[n] Ex. h[n] = { 5, 6, 7, 8 }
Infinite Length Finite Length
Causal Causal
STABLE STABLE
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NOTE : To find Output of Digital Filter
✔
✔ (1) h[n]
?
x[n] (2) H[z] y[n]
(3) DE
(4) RD
(5) PZ
ZT IZT
(6) FR
X(z) Y(z)
H(z)
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NOTE : Relationship Diagram
1. Take ZT
2. Arrange in terms of
Y(z) & X(z) PZ
3. Write H(z) =Y(z) / X(z)
IZT
DE H(z) h[n]
ZT
Z=ejw
1. Write H(z) in –ve H(ejw) OR
Powers of Z RD H(w)
2. Let H(z) = Y(z)/X(z)
3. Cross multiply
4. Take Inverse ZT
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1. What is Digital filter ?
* DT System *
x[n] y[n]
Ex. Digital Filter
Digital filter is nothing but a
Mathematical Algorithm
implemented in hardware or
software.
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(2) What are the Advantages of
Digital Filters ?
Ans :
• A Digital filter is Programmable,
• Digital filters can be easily Designed,
Tested and Implemented
• Digital Filters are extremely stable with
respect both to time and temperature.
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(3) Compare FIR filters and IIR filters
• FIR filter • IIR filter
1 Provides exact Linear Phase. NO Linear Phase.
2 Provides good stability. Stability is not guaranteed.
3 Order required is higher. Order required is lower.
4 Computationally not efficient. Computationally more efficient.
5 More memory required for Less memory required fro
the storage of coefficients. storage of coefficients.
6 Requires more processing time. Requires less processing time.
7 Requires N Multiplications Requires 2N + 1 Multi. per
per output sample output sample.
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(4) What are the advantages of FIR
Filters (compared to IIR
filters)?
Ans :
• They can be designed with “Linear Phase"
• They are suited to multi-rate applications.
• They have desirable numeric properties.
• They can be implemented using fractional arithmetic.
• They are always stable.
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(5) What are the disadvantages of FIR
Filters (compared to IIR filters)?
Ans : FIR filters require more memory and
calculations to achieve a given filter
response characteristic
(6) What are the advantages of IIR Filters
(compared to IIR filters)?
Ans : IIR filters require Less memory and
calculations to achieve a given filter
response characteristic
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(8) Why IIR filters are called as recursive
filters ?
Ans : In IIR filter output dépends on output values.
e.g. y[n] = x[n] + x[n-1] + y[n] + y[n-1].
Therefore IIR filters are also called as
Recursive Filters
(9) Why FIR filters are called as NON
recursive filters ?
Ans : In FIR filter output dépends only on Input values.
e.g. y[n] = x[n] + x[n-1]
Therefore FIR filters are also called as
Non-Recursive Filters
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9/10/2024
(10) What is Minimum Phase System ?
For any system If H() – H(0) = 0
Then system is called a Minimum Phase System.
When All zeros are inside the unit circle, the
system is minimum phase.
(11) What is Maximum Phase System ?
For any system If H() – H(0) = M
Then system is called a Maximum Phase System.
When All zeros are outside the unit circle, the system is
Maximum phase.
NOTE :
If the system is Neither Minimum Phase
NOR Maximum Phase
Then System is Mixed Phase System.
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Ideal Filter Frequency Response
LPF HPF
PB SB SB PB
BPF BSF/BRF
SB PB SB PB SB PB
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Practical Filter Frequency Response
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I I R FILTER DESIGN
Time Domain Transform Domain
Method Method
Impulse Invariant Method BLT Method
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IIR Filters
Infinite impulse response (IIR) filter is described using :
(a) IIR filter difference equation
IIR filter output
depends also on
(b) IIR filter Transfer function the past outputs
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F I R FILTER DESIGN
Windowing Method Frequency Sampling Method
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Difference between between Analog Filter and Digital Filter
Parameter Analog filter Digital Filter
1 Digital(discrete time
Input/output signal Analog
sequences)
2 Lumped elements such as Software + digital
Composition
R.L. and C or analog /Cs hardware
3 In terms of system By difference
Filter representation
components equation
4 Flexibility Not flexible Highly flexible
5 Portability Not easily portable Portable
6 Design objective and Specifications to values of Specifications to
result R.L and C components difference equation
7 Environmental effects Negligible effect of Negligible effect of
environmental parameters environmental
parameters
8 Interference notes Minimum/negligible
Maximum effect
and other effects effect
9 Storage/maintenance Difficult storage and Easier storage and
failure maintenance and higher maintenance and
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failure rate reduced failure rate
Difference between between IIR Filter and FIR Filter
FIR filter IIR filter
1 Length of h[n] is finite Length of h[n] is In-finite
2 Provides exact linear phase. Not linear phase.
3 Provides good stability. Stability is not guaranteed.
4 Order required is higher. Order required is lower.
5 Computationally not efficient. Computationally more efficient.
6 More memory required for the Less memory required fro storage of
storage of coefficients. coefficients.
7 Requires more processing time. Requires less processing time.
8 Requires M multiplications per Requires 2M + 1 multiplications per
output sample output sample.
Dr. Kiran TALELE 9987030881 talelesir@gmail.com
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Dr. Kiran TALELE
Academic : PhD
Professional :
Dean-Students, Alumni & External Relations
@ Bharatiya Vidya Bhavans’ Sardar Patel
Institute of Technology (SP-IT), Mumbai
Co-ordinator @ Sardar Patel Technology
Business Incubator (SP-TBI), Mumbai
Treasurer-IEEE Bombay Section
091-9987030881 www.talelesir.com talelesir@gmail.com
https://www.linkedin.com/in/k-t-v-talele/
www.facebook.com/Kiran-Talele-1711929555720263
Stay Connected
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9/10/2024
• Dr. Kiran TALELE is an Associate Professor in Electronics &
Telecommunication Engineering Department of Bharatiya Vidya Bhavans’
Sardar Patel Institute of Technology, Mumbai with 33+ years experience in
Academics.
• He is a Dean of Students, Alumni and External Relations at Sardar Patel
Institute of Technology, Andheri Mumbai. He is also a Co-ordinator of Sardar
Patel Technology Business Incubator, Mumbai.
• His area of research is Digital Signal & Image Processing, Computer Vision,
Machine Learning and Multimedia System Design.
• He has published 85+ research papers at various national & international
refereed conferences and journals. He has published 22 patents at Indian
Patent Office. One patent is granted in 2021.
• He is a Treasurer of IEEE Bombay Section and Mentor for Startup Incubation &
Intellectual Asset Creation.
• He received incentives for excellent performance in academics
and research from Management of S.P.I.T. in 2008-09. He is a recipient of
P.R. Bapat IEEE Bombay Section Outstanding Volunteer Award 2019.
