ELE 792 Midterm: ELE 792 Fall 2017 Midterm
31 Jan 2019
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October 25, 2017: this is a open book / open notes exam, return this paper at the end of your examination, no computers are permitted except for viewing lecture notes, start time: 16:10 end time: 18:00. You are asked to implement a lpf with stopband frequency /8. Let g(z) be the transfer function of this lter with input x[n] and output y[n]. The sampling frequency for both the input sequence x[n] and the output sequence y[n] is fs = 2 khz. G(z) you can use the lters h2(z), h4(z) and h8(z) multiple times. You also have access to an unlimited number of down-by-two downsamplers and up-by-two upsamplers. Determine all possible implementations of g(z) using the available resources ( lters, up- samplers and downsamplers). Determine the number of multiplications per unit time that each implementation requires. Identify the most ef cient implementation which minimizes the number of multiplications required per unit time.
