Infinite Impulse Response IIR Filter Design A Give the name

Infinite Impulse Response (IIR) Filter Design A. Give the name of the three most commonly used techniques for designing IIR filters. (The Butterworth method is one of them.) Each of them gives an optimum design according to some criteria. State that criteria for each of them. B. The technical for designing a digital filter is to design an analog filter (in the s-domain) and then convert from the s-domain to the z-domain to obtain a digital filter. Give the two techniques for converting from the s-domain to the z-domain.

Solution

G A)

Butterworth filter: magnitude response of this filter decrease monotonically as the frequency increases. Pole of Butterworth filter lies on a circle. Transition band is more in Butterworth.

Type I Chebyshev Fitee: it is all pole filters that exhibits equiripple behaviour in the passband and a monotonic chatacteristic in the stop band. ploe of this filter lies on ellipse.for same specification number of poles in this filter is less compared to Butterworth filter ,that is order of chebysev filter is less than the Butterworth.

Type II Chebyshev Filter: it contains both poles and zeros and exhibits a monotonic behaviour in the passband and equiripple behaviour in the stop band.

(B) two methods used for digitizing the analog into digital filter .

1. Approximation of derivation:  it analog to digital transform maps a stable analog into a stable digital filter , but jw axis does not even map on to the z= e^(jw) circle. This transform restricts the digital filter pole locations that are confined to relatively small frequencies.

Maping from analog to digital can be achieved by

S=(1-z^-1)/T

2 bilinear transform: this transform is co formal mapping that transform the jw axis into the unit circle in z plane. , all the points in the LHP of \'s\' are mapped inside the unit circle in the z plane and all the points in the RHP of \'s\' are mapped into corresponding outside the unit circle in z plane.

Mapping of s plane to z plane can be obtained as

S = (2/T)(1-z^-1)/(1+z^-1)