090114Lecture05

# 090114Lecture05 - ECE 700 Digital Signal Processing Lecture...

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ECE 700 ECE 700 WI 2009 Digital Signal Processing Lecture 5 01/14/09 1

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The Noble Identities L ( ) L H z ( ) H z L Noble Identity 1 ECE 700 WI 2009 Noble Identity 2 M ( ) M H z ( ) H z M 2
Polyphase Interpolation 1 0 1 ( ) ( ) ( ) ( ( ) ) ( ) ( ) ( ) L L p p p L L p p Y z H z V z H z z V z H z V z z - - = - - = = = ECE 700 WI 2009 0 p = 3

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Polyphase decimation 1 0 1 ( ) ( ) ( ) ( ( ) ) ( ) ( )( ( )) M M p p p M M p V z H z X z H z z X z H z z X z - - = - - = = = ECE 700 WI 2009 4 0 p p =
Computational considerations Suppose H ( z ) is implemented using a FIR lowpass filter with N taps. For decimation by a factor of M , we have NM multiplies/output sample. For a polyphase implementation of H ( z ), we have M branches, ECE 700 WI 2009 each with N / M taps. So number of multiplies/output sample is N . Dependence on M enters via the required filter length, since is linearly propotional to / , so is also linearly propotional to . M N M ϖ π 5

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## This note was uploaded on 04/18/2009 for the course ECE 700 taught by Professor Un during the Winter '09 term at Ohio State.

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090114Lecture05 - ECE 700 Digital Signal Processing Lecture...

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