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UNIT III – IIR FILTER DESIGN
1. What are the different types of filters based on impulse response?
Based on impulse response the filters are of two types
1. IIR filter
2. FIR filter
The IIR filters are of recursive type, whereby the present output sample depends on the
present input, past input samples and output samples.
The FIR filters are of non recursive type, whereby the present output sample depends on
the present input sample and previous input samples.
2. What are the different types of filters based on frequency response?
Based on frequency response the filters can be classified as
1. Lowpass filter
2. Highpass filter
3. Bandpass filter
4. Bandreject filter
3. What are the advantages and disadvantages of FIR filters?
Advantages:
1. FIR filters have exact linear phase.
2. FIR filters are always stable.
3. FIR filters can be realized in both recursive and non recursive structure.
4. Filters with any arbitrary magnitude response can be tackled using FIR sequence.
Disadvantages:
1. For the same filter specifications the order of FIR filter design can be as high as 5 to 10
times that in an IIR design.
2. Large storage requirement is requirement
3. Powerful computational facilities required for the implementation.
4. How one can design digital filters from analog filters?
· Map the desired digital filter specifications into those for an equivalent analog filter.
· Derive the analog transfer function for the analog prototype.
· Transform the transfer function of the analog prototype into an equivalent digital filter
transfer function.
5. Mention the procedures for digitizing the transfer function of an analog filter.
The two important procedures for digitizing the transfer function of an analog filter are
· Impulse invariance method.
· Bilinear transformation method.
. Approximation of derivatives
6. Distinguish between FIR filters and IIR filters.
FIR filter IIR filter
These filters can be easily designed to have These filters do not have linear phase.
perfectly linear phase.
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FIR filters can be realized recursively and non- IIR filters are easily realized recursively
recursively.
Greater flexibility to control the shape of their Less flexibility, usually limited to specific kind
magnitude response. of filters.
Errors due to round off noise are less severe in The round off noise in IIR filters is more.
FIR filters, mainly because feedback is not
used.
7. What do you understand by backward difference?
One of the simplest methods for converting an analog filter into a digital filter is to
approximate the differential equation by an equivalent difference equation.
d/dt y(t)=y(nT)-y(nT-T)/T
The above equation is called backward difference equation.
8. What is the mapping procedure between S-plane & Z-plane in the method of mapping
differentials? What are its characteristics?
The mapping procedure between S-plane & Z-plane in the method of mapping of
differentials is given by
H(Z) =H(S)|S=(1-Z-1)/T
The above mapping has the following characteristics
· The left half of S-plane maps inside a circle of radius ½ centered at Z= ½ in the Zplane.
· The right half of S-plane maps into the region outside the circle of radius ½ in the
Z-plane.
· The j .-axis maps onto the perimeter of the circle of radius ½ in the Z-plane.
9. What is meant by impulse invariant method of designing IIR filter?
In this method of digitizing an analog filter, the impulse response of the resulting digital
filter is a sampled version of the impulse response of the analog filter. If the transfer function is
of the form, 1/s-p, then
H (z) =1/1-e-pTz-1
10. What is bilinear transformation?
The bilinear transformation is a mapping that transforms the left half of S-plane into the
unit circle in the Z-plane only once, thus avoiding aliasing of frequency components. The
mapping from the S-plane to the Z-plane is in bilinear transformation is
S=2/T(1-Z-1/1+Z-1)
11. What are the properties of bilinear transformation?
· The mapping for the bilinear transformation is a one-to-one mapping that is for every
point Z, there is exactly one corresponding point S, and vice-versa.
· The j .-axis maps on to the unit circle |z|=1,the left half of the s-plane maps to the interior
of the unit circle |z|=1 and the half of the s-plane maps on to the exterior of the unit
circle |z|=1.
12. Write a short note on pre-warping.
The effect of the non-linear compression at high frequencies can be compensated. When
the desired magnitude response is piece-wise constant over frequency, this compression can be
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compensated by introducing a suitable pre-scaling, or pre-warping the critical frequencies by
using the formula.
13. What are the advantages & disadvantages of bilinear transformation?
Advantages:
· The bilinear transformation provides one-to-one mapping.
· Stable continuous systems can be mapped into realizable, stable digital systems.
· There is no aliasing.
Disadvantage:
· The mapping is highly non-linear producing frequency, compression at high frequencies.
· Neither the impulse response nor the phase response of the analog filter is preserved in a
digital filter obtained by bilinear transformation.
14. Distinguish analog and digital filters
Analog Filter Digital Filter
Constructed using active or passive components Consists of elements like adder, subtractor
and it is described by a differential equation and delay units and it is described by a
difference equation
Frequency response can be changed by Frequency response can be changed by
changing the components changing the filter coefficients
It processes and generates analog output Processes and generates digital output
Output varies due to external conditions Not influenced by external conditions
15. What are the properties of chebyshev filter?
1. The magnitude response of the chebyshev filter exhibits ripple either in the stop band or
the pass band.
2. The poles of this filter lies on the ellipse
16. List the Butterworth polynomial for various orders.
N Denominator polynomial
1 S+1
2 S2+.707s+1
3 (s+1) (s2+s+1)
4 (s +.7653s+1) (s2+1.84s+1)
2
5 (s+1) (s2+.6183s+1) (s2+1.618s+1)
6 (s2+1.93s+1) (s2+.707s+1) (s2+.5s+1)
7 (s+1) (s2+1.809s+1) (s2+1.24s+1) (s2+.48s+1)
17. Differentiate Butterworth and Chebyshev filter.
Butterworth damping factor 1.44 chebyshev 1.06
Butterworth flat response damped response.
18. What is filter?
Filter is a frequency selective device, which amplifies particular range of frequencies and
attenuate particular range of frequencies.
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PART B
1. a) Derive bilinear transformation for an analog filter with system function
H(S) = b/S + a
b) Discuss the limitation of designing an IIR filter using impulse invariant method
2. Determine H (Z) for a Butterworth filter satisfying the following specifications:
Assume T= 0.1 sec. Apply bilinear transformation method
3. Determine digital Butterworth filter satisfying the following specifications:
Assume T= 1 sec. Apply bilinear transformation method.
4. Design a Chebyshev low pass filter with the specifications dB ripple in the pass band
dB ripple in the stop band using impulse invariance method
5. Design a Butterworth high pass filter satisfying the following specifications.
6. Design a Butterworth low pass filter satisfying the following specifications.
7. Design (a) a Butterworth and (b) a Chebyshev analog high pass filter that will pass all radian
frequencies greater than 200 rad/sec with no more that 2 dB attuenuation and have a stopband
attenuation of greater than 20 dB for all less than 100 rad/sec.
8. Design a digital filter equivalent to this using impulse invariant method
H(S) = 10/S2+7S+10
9. Use impulse invariance to obtain H(Z) if T= 1 sec and H(s) is
10. Use bilinear transformation method to obtain H (Z) if T= 1 sec and H(s) is
11. Briefly explain about bilinear transformation of digital filter design
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12. Compare bilinear transformation and impulse invariant mapping
13. Design a chebyshev filter with a maxmimum pass band attenuation of 2.5 Db; at Ωp=20
rad/sec and the stop band attenuation of 30 Db at Ωs=50 rad/sec.
14. Describe various Structures of IIR filter Design
15. Realize the system given by difference equation -0.1y (n-1)+0.72y(n-2)+0.7x(n)-0.25x(n-2)
in parallel form
16. Design a butterworth high pass filter satisfying
Fp = 0.32, αp=0.5db, Fs= 0.16Hz, αs=30db, F=1Hz
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