Where does the poles of the system function of the second filter locate?(a) e^j2π(k+α)M(b) e^j2π(k+α)/M(c) e^j2π(k-α)/M(d) e^jπ(k+α)/MThis question was addressed to me in semester exam.Enquiry is from Structures for FIR Systems in chapter Discrete Time Systems Implementation of Digital Signal Processing

Where does the poles of the system function of the second filter locat

1.	Where does the poles of the system function of the second filter locate?(a) e^j2π(k+α)M(b) e^j2π(k+α)/M(c) e^j2π(k-α)/M(d) e^jπ(k+α)/MThis question was addressed to me in semester exam.Enquiry is from Structures for FIR Systems in chapter Discrete Time Systems Implementation of Digital Signal Processing
Answer» Right option is (B) e^j2π(k+α)/M For explanation I would SAY: The system function of the SECOND filter in the cascade of an FIR realization by frequency sampling method is given by H2(Z)=\(\sum_{k=0}^{M-1} \frac{H(k+α)}{1-e^{\frac{j2π(k+α)}{M}} z^{-1}}\) We obtain the poles of the above system function by equating the denominator of the above EQUATION to zero. =>\(1-e^{\frac{j2π(k+α)}{M}} z^{-1}\)=0 =>z=pk=\(e^{\frac{j2π(k+α)}{M}}\), k=0,1….M-1

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