1.8 Polyphase interpolation

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 ismostly composed of zeros. Through the use of the Noble identities, it is possible to rearrange the preceding blockdiagram 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 $H_p(z^L)$ , $p=\{0, \dots , L-1\}$ .

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.