Repeat Illustrative Problem 9.5 when the tap weight coefficients are generated by a single-pole…

Repeat Illustrative Problem 9.5 when the tap weight coefficients are generated by a single-pole lowpass filter described by the z-transform

Problem 9.5

Generation of Tap Weight Coefficients] Let us use a simple digital IIR filter that is excited by complex-valued white Gaussian noise to generate a sampled version of a channel tap weight coefficients. The lowpass IIR filter with two identical poles is described by the z-transform

where { Wn = Wnr + }Wni} is the input AWGN sequence, { Cn} is the output sequence, and 0 < p="">< 1="" is="" the="" pole="" position.="" the="" position="" of="" the="" pole="" controls="" the="" bandwidth="" of="" the="" filter="" and,="" hence,="" the="" rate="" of="" variations="" of="" {en}.="" when="" p="" is="" close="" to="" the="" unit="" circle,="" the="" filter="" bandwidth="" is="" narrow,="" whereas="" when="" p="" is="" close="" to="" zero,="" the="" bandwidth="" is="" wide.="" generate="" 1000="" samples="" of="" {en="Cnr" +}end="" when="" p="0.9" and="" p="0.99," and="" plot="" {cnr},="" {end="" and="" {i="" cn="" i}="" for="" each="" value="" of="" p.="" also,="" compute="" and="" plot="" the="" power="" spectrum="" and="" the="" autocorrelation="" function="" of="" {="" cn}="" for="" the="" two="" values="" of="">