12/4/2023
Introducton to Digital Filter
@
Sardar Patel Institute of
Technology, Andheri, Mumbai
Kiran TALELE
Academic Year 2023-24
Bharatiya Vidya Bhavans’
Sardar Patel Institute of Technology Andheri(w) Mumbai
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)
ZT h[n]
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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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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(*) 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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(*) 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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(*) 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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(*) 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
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(*) 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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(*) 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
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(*) 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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(*) What is Magnitude Response ?
Ans :
Magnitude = Magnitude of numerator
Response Magnitude of Deno min ator
Where,
Magnitude (Re al ) 2 (Im aginary ) 2
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(*) What is Phase Response?
Ans :
Phase = Angle of – Angle of
Response Numerator Denominator
Where, 1 Im aginary
tan Re al When Re al 0
Angle
1 Im aginary
180 tan When Re al 0
Re al
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(*) What is stability condition for
causal and stable system?
Ans :
.
For causal and stable
system, all the POLES
must lie INSIDE the unit
circle
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(*) 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.
(*) 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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DSP System
x(t) x(n) y(n) Reconstruction y(t)
Sampling A D
x[n]
Using S/H Digital FILTERA
DDigital Processor y[n]
Using LPF
C C
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DSP System . . .
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Digital filter is nothing but
a Mathematical Algorithm
implemented in
Hardware or Software.
Kiran TALELE 9987030881
IMPORTANT
•An important step in the development of a
digital filter is the determination of a
realizable transfer function H(z)
approximating the given frequency
response specifications. The process of
deriving the transfer function H(z) is called
digital filter design.
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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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Digital 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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Digital 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
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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.
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Q1 What are advantages of FIR Filters ?
1. They can easily be designed to be "linear
phase"
2. They are suited to multi-rate applications.
3. They have desirable numeric properties.
4. They can be implemented using fractional
arithmetic.
5. They are simple to implement.
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Q2 . What are the disadvantages of FIR Filters
(compared to IIR filters)?
Compared to IIR filters, FIR filters sometimes have the
disadvantage that they require more memory and/or
calculation to achieve a given filter response
characteristic.
Q3. What are the advantages of IIR filters (compared
to FIR filters)?
IIR filters can achieve a given filtering characteristic using
less memory and calculations than a similar FIR filter
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Q4 . What are the disadvantages of IIR Filters
(compared to FIR filters)?
1) They are more susceptible to problems of finite-
length arithmetic, such as noise generated by
calculations, and limit cycles.
2) They are harder to implement using fixed-point
arithmetic.
3) They don't offer the computational advantages of
FIR filters for multirate (decimation and
interpolation) applications.
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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
Head-Academic Relation @ Sardar Patel
Technology Business Incubator (SP-TBI),
Mumbai
Treasurer-IEEE Bombay Section
091-9987030881
kiran.talele@spit.ac.in / ktvtalele@gmail.com
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