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FIR Filters - Elliptical

Verification of the designed filter is carried out by testing impulse response and step response. Simulation waveform of the both step and impulse response is shown in Figure | Chapter Elliptical Filters By allowing ripples in the pass band Chebyshev filters obtain better selectivity than Butterworth filters do. Elliptical filters improve upon the performance of Chebyshev filters by permitting ripples in both the pass band and stop band. The response of an elliptical filter satisfies where 2 n y L is an nth-order Chebyshev rational function with ripple parameter L. Elliptical filters are sometimes called Cauer filters. 5.1 Parameter Specification As shown in Chap. 3 determination of the amplitude-normalized transfer function for a Butterworth lowpass filter requires specification of just two parameters cutoff frequency oc and filter order n. Determination of the transfer function for a Chebyshev filter requires specification of these two parameters plus a third pass-band ripple or stop-band ripple for inverse Chebyshev . Determination of the transfer function for an elliptical filter requires specification of the filter order n plus the following four parameters which are depicted in Fig. 5.1 Ap maximum pass-band loss dB As minimum stop-band loss dB pass-band cutoff frequency a s stop-band cutoff frequency The design procedures presented in this chapter assume that the maximum pass-band amplitude is unity. Therefore Ap is the size of the pass-band 93 94 Chapter Five Figure 5.1 Frequency response showing parameters used to specify an elliptical filter. ripples and As is the size of the stop-band ripples. Any four of the five filter parameters can be specified independently with the fifth then being fixed by the nature of the elliptical filter s response. The usual design strategy involves specifying Ap As a p and a s based upon requirements of the intended application. Algorithm 5.1 as follows can then be used to compute the minimum value of n for which an elliptical filter can yield the desired performance. Since n must be an integer not all combinations of Ap As op and a s can be realized exactly. The design procedure presented in this .