(b) The second circuit is an active filter. If Z, is a capacitor C, and Z, is a parallel RC circuit, with elements R and C (this C has the same value as the C in Z, ), determine an expression for the voltage transfer function. Write your result in the form: « (@) _ 1+ jAo V„ (0) 1+ jBo H(@) out in (i.e., define A and B in terms of R and C). Vin out Z,

4. (a) IIR filters offer the possibility to achieve magnitude response specifications with a smaller number of coefficients than required for FIR filters. Despite this, designers often prefer to use FIR filters. Explain one reason why they have this preference. (b) You have designed Butterworth, Chebyshev, and Elliptic IIR filters so that the magnitude response satisfies 0.98 < |H(w)| < 1.02 for 0 < w < 0.2n and satisfies H(w) < 0.01 for 0.257 < w < T. With Nhutter, Neheby, and Netlip denoting the transfer function orders of the Butterworth, Chebyshev, and Elliptic filters, respectively, which of the following relationships is expected to hold among them? Nhutter < Neheby < Nettip Nbutter < Nellip < Ncheby Neheby < Niutter < Nellip Ncheby < Neltip < Nhutter Nellip < Nhutter S Ncheby Nellip < Ncheby< Noutter (c) You are designing an analog IIR filter that you will convert using the bilinear transformation to a digital filter. Your digital filter will have a sampling rate of 5000 Hz, and…