Asecond-order recursivenotchfilter is illustrated inFig.1.Thefilterhasanullatthefrequency0.05 cycles/sample(equivalently, 0.1radians/sample). Thepoleshaveamodulusof0.9.Thefilter isnormalizedsothedcgain isunity, as evident inthe plot. But thegainonthehigh-frequencysideexceedsunity, reaching1.11. Task: Designa third-order recursivenotchfilter withanull at the same frequency. Thenewfiltershouldhaveagainofunityatbothf=0and f =0.5 cycles/sample. The dierence equation shouldhavereal-valuedcoe cients. There ismore thanonecorrectsolution. The frequencyresponse magnitudeofonesolutionisillustratedinFig. 2. To submit: Mathematical derivation, dierence equationcoe cients,pole-zerodiagram, frequency responsemagnitude,andMatlabcode. 1.5 1 0.5 0 0.5 1 1.5 1 0.5 0 0.5 1 Real Part Imaginary Part Pole/zero diagram 0 0.1 0.2 0.3 0.4 0.5 0 0