Polyphase Interpolation 2.11 2002/01/04 2005/10/18 20:03:38.683 GMT-5 Phil Schniter schniter@ee.eng.ohio-state.edu Adan Galvan jago@rice.edu Erin Maloney emaloney@rice.edu Phil Schniter schniter@ee.eng.ohio-state.edu interpolation polyphase Implementation of a polyphase interpolation filter.

Polyphase Interpolation Filter Recall the standard interpolation procedure illustrated in .

Note that this procedure is computationally inefficient because the lowpass filter operates on a sequence that is mostly composed of zeros. Through the use of the Noble identities, it is possible to rearrange the preceding block diagram so that operations on zero-valued samples are avoided. In order to apply the Noble identity for interpolation, we must transform H z into its upsampled polyphase components H p z L , p 0 … L 1 . H z n n h n z n k k p 0 L 1 h k L p z k L p via ≔ k n L , ≔ p n L H z p 0 L1 k k h p k z k L z p via ≔ h p k h k L p H z p 0 L1 H p z L z p Above, · denotes the floor operator and · M the modulo-M operator. Note that the pth polyphase filter h p k is constructed by downsampling the "master filter" h n at offset p. Using the unsampled polyphase components, the diagram can be redrawn as in .

Applying the Noble identity for interpolation to yields . The ladder of upsamplers and delays on the right below accomplishes a form of parallel-to-serial conversion.