m10433 Polyphase Decimation Filter 2.12 2002/01/07 2009/06/01 15:34:39.005 GMT-5 Phil Schniter Phil Schniter schniter@ee.eng.ohio-state.edu Phil Schniter Phil Schniter schniter@ee.eng.ohio-state.edu Adan Galvan Adan Galvan agalvan@gmail.com Erin Maloney Erin Maloney emaloney@rice.edu Phil Schniter Phil Schniter schniter@ee.eng.ohio-state.edu decimation interpolation Kaiser polyphase Science and Technology Implementation of polyphase decimation filters. en

Recall the standard decimation method in .

Note that this procedure is computationally inefficient because it discards the majority of the computed filter outputs. Through the use of the Noble identities, it is possible to rearrange so that filter outputs are not discarded. In order to apply the Noble identity for decimation, we must transform Hz into its upsampled polyphase components H p z M , p 0 … M 1 , defined previously in the context of polyphase interpolation. H z n n h n z n k k p 0 M 1 h k M p z k M p via ≔ k n M , ≔ p n M H z p 0 M1 k k h p k z k M z p via ≔ h p k h k M p H z p 0 M1 H p z M z p Using these unsampled polyphase components, the preceding block diagram can be redrawn as .

Applying the Noble identity for decimation to yields . The ladder of delays and downsamplers on the left below accomplishes a form of serial-to-parallel conversion.