A high-pass filter (HPF) is defined over its transfer function as Hµpf(z) = K 1 a) Find the constant K that normalizes the filter gain such that |Hypf(e^)| = 1 while N = n at high-frequencies. 1+0.5z-1" b) Sketch pole-zero diagram of this filter. c) Roughly sketch the corresponding magnitude response |HµpF(e^)|. Note that |Hµpf(e^)| = 0 for N = 0.

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1-z-1
A high-pass filter (HPF) is defined over its transfer function as HHpf(z) = K ;
1+0.5z-1
a) Find the constant K that normalizes the filter gain such that |HypF(e^)| = 1 while N = n at high-frequencies.
HPF
b) Sketch pole-zero diagram of this filter.
c) Roughly sketch the corresponding magnitude response |Hµpf(e^)|. Note that |HupF(e)|= 0 for 2 = 0.
HPF
HPF
Transcribed Image Text:1-z-1 A high-pass filter (HPF) is defined over its transfer function as HHpf(z) = K ; 1+0.5z-1 a) Find the constant K that normalizes the filter gain such that |HypF(e^)| = 1 while N = n at high-frequencies. HPF b) Sketch pole-zero diagram of this filter. c) Roughly sketch the corresponding magnitude response |Hµpf(e^)|. Note that |HupF(e)|= 0 for 2 = 0. HPF HPF
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