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IIR Filter Design Techniques

This document discusses IIR filter design. It begins by defining IIR filters as systems with an infinite impulse response. It then lists techniques for converting continuous-time analog filters to digital filters, including impulse invariance, bilinear transformation, and approximation of derivatives. It defines frequency warping as the nonlinear mapping between frequency variables in the continuous and discrete domains. The document outlines various IIR system structures like direct form I and II and cascade realization. It provides the mathematical expression for an IIR system and lists disadvantages of the impulse invariance method. It defines Gibbs phenomenon and the bilinear transformation. It gives two properties of Butterworth lowpass filters and lists the basic IIR system structures.

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Jagan Faith
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88 views2 pages

IIR Filter Design Techniques

This document discusses IIR filter design. It begins by defining IIR filters as systems with an infinite impulse response. It then lists techniques for converting continuous-time analog filters to digital filters, including impulse invariance, bilinear transformation, and approximation of derivatives. It defines frequency warping as the nonlinear mapping between frequency variables in the continuous and discrete domains. The document outlines various IIR system structures like direct form I and II and cascade realization. It provides the mathematical expression for an IIR system and lists disadvantages of the impulse invariance method. It defines Gibbs phenomenon and the bilinear transformation. It gives two properties of Butterworth lowpass filters and lists the basic IIR system structures.

Uploaded by

Jagan Faith
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as DOC, PDF, TXT or read online on Scribd
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UNIT II IIR FILTER DESIGN

1. What is IIR filters?


If the unit sample response of a linear shift invariant sytem is of infinite
duration, the system is said to be an infinite impulse response (IIR) system.

2. Mention the various techniques are used in continous-time analog filter into digital
filter.
(a) Impulse Invariance technique.
(b) Bilinear transformation.
(c) Approximation of derivatives.
(d) Butterworth filters.

3. Define frequency warping.

 T 
  2 tan 1  
 2 
Relationship between two frequency variables in the two domains.The
variables in the two domains. The entire range in Ω is mapped only once into the
range -      .
How ever, the mapping is highly nonlinear. We observe a frequency compression or
frequency warping as it is usually called ,due to the nonlinearity of the arctangent
function.

4. Specify the various structure of an IIR system.


(a) Direct-form I realization .
(b) Direct-form II realization.
(c) Cascade realization.

5. Write down the mathematical expression for an IIR system.


An analog filter can be described by it’s system function
M

B(S )
 k Sk
H a (S )   k 0
N ------------- (1)
A( S )

k 0
k S k

Where {  k }and {  k } are the filter co-efficients,or by it’s impulse response ,which
is
related to H a (S ) by the Laplace transform

6.What are the disadvantages of Impulse invariance method?


This method is unsuccessful for implementing digital filters for which |H(jw)| does not
approaches zero for large values of w (I t is not applicable for high pass, band pass
design)
7. What is Gibbs phenomenon?
In the design of FIR filter the infinite duration impulse response is truncated in to
finite duration impulse response this abrupt truncation introduces oscillations in pass
band and stop band .This effect is known as Gibbs phenomenon.

8. What is Bilinear transformation?


It is a conformal mapping that transforms the j  axis into the unitcircle in the
Z- plane only once, thus avoiding aliasing of frequency components.
Furthermore ,all points in the LHP of s are mapped inside the unitcircle in the
Z-plane and all points in the RHP of S are mapped into corresponding points outside
the Z-plane.
2  1  Z 1 
Clearly, the mapping from the S-plane to Z-plane is S   
T  1  Z 1 
This is called bilinear transformation.

9. Give any two properties of Butterworth lowpass filter.


a. The magnitude response of the Butterworth filter decreases monotonically as
the frequency Ω increases from 0 to infinity.
b. The magnitude response of the Butterworth filter closely approximates the ideal
response as the order N increases.
c. The poles of the Butterworth filter lies on a circle.

10. Mention the basic structures for IIR systems.


a. Direct Form I
b. Direct Form II
c. Cascade Realization
d. Parallel Realization and
e. Transposed Forms.

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