TRANSITIONAL BUTTERWORTH-CHEBYSHEV FILTERS
- 1. TRANSITIONAL BUTTERWORTH- CHEBYSHEV FILTERS DIGITAL SIGNAL PROCESSING NAME – NITHIN KALLEPALLY
- 2. Transitional Butterworth - Chebyshev filters These filters have properties that lie between those of the Butterworth and Chebyshev filters. So it is appropriate to call this kind of filters as transitional Butterworth-Chebyshev filters.
- 3. These design technique for transitional Butterworth-Chebyshev filters is described. It offers two advantageous features ; (i) the degree of flatness at ω = 0 increases with decreasing number of passband rippled and (ii) the transition is gradual and complete.
- 4. BUTTERWORTH FILTER Butterworth Filter Approximation ◦ The magnitude response of a Butterworth filter is Shown in the figure ◦ The magnitude response of low pass butterworth filter is given by ◦ FIG- magnitude response of lowpass butterworth filter
- 5. The Poles Equation ◦ If the poles are complex conjugate then organize the poles ( P k) as complex conjugate pairs that means s1 and , s2 and etc . System Transfer Function Of Analog Filter Equation ◦ ◦ And if poles are complex conjugate then,
- 6. CHEBYSHEV FILTER ◦ Using Chebyshev filter design, there are two sub groups, ◦ Type-I Chebyshev Filter: ◦ These filters are all pole filters. In the pass band, these filters show equiripple behavior and they have have monotonic characteristics in the stop band. ◦ The filter characteristics is shown in fig ◦ Type-II Chebyshev Filter: ◦ These filters contains zeros as well as poles. ◦ In the stop band, these filters show equiripple behavior and they have monotonic characteristics in the pass band. ◦ The major difference between butterworth and chebyshev filter is that the poles of butterworth filter lie on the circle while the poles of chebyshev filter lie on ellipse
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