Find the matrices E ( z ) and R ( z ) for the filter bank described by Equations (9.131)–

Find the matrices E ( z ) and R ( z ) for the filter bank described by Equations (9.131)– (9.134), and verify that their product is equal to a pure delay.

Modify the causal analysis and synthesis filters of the filter bank in equations (9.131)– (9.134) so that they constitute a zero-delay perfect reconstruction filter bank. Do the same for the filter banks in Equations (9.135)–(9.138). Suggest a general method to transform any perfect reconstruction causal filter bank into a zero-delay filter bank.

 

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