Given the lowpass analysis filter of a two-band FIR perfect reconstruction filter bank [H_{0}(z)=z^{-3}+a z^{-2}+b z^{-1}+2] determine

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Given the lowpass analysis filter of a two-band FIR perfect reconstruction filter bank

\[H_{0}(z)=z^{-3}+a z^{-2}+b z^{-1}+2\]

determine the analysis and synthesis filters and discuss the class of filter bank to which they belong. Deduce the relation between \(a\) and \(b\), assuming they are nonzero, in order to achieve perfect reconstruction.

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