Skip to content Skip to navigation

Connexions

You are here: Home » Content » Polyphase Resampling with a Rational Factor

Navigation

Content Actions
  • Download module PDF
  • Add to ...
    Add the module to:
    • My Favorites
    • A lens
    • An external social bookmarking service
    • My Favorites (What is 'My Favorites'?)
      'My Favorites' is a special kind of lens which you can use to bookmark modules and collections directly in Connexions. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need a Connexions account to use 'My Favorites'.
    • A lens (What is a lens?)

      Definition of a lens

      Lenses

      A lens is a custom view of Connexions content. You can think of it as a fancy kind of list that will let you see Connexions through the eyes of organizations and people you trust.

      What is in a lens?

      Lens makers point to Connexions materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

      Who can create a lens?

      Any individual Connexions member, a community, or a respected organization.

    • External bookmarks
  • E-mail the author

Recently Viewed

This feature requires Javascript to be enabled.

Polyphase Resampling with a Rational Factor

Module by: Phil Schniter

Summary: Introduction to the concept of Polyphase Resampling.

Polyphase Resampling with a Rational Factor

Recall that resampling by rational rate LM LM can be accomplished through the following three-stage process(see Figure 1).

Figure 1
Figure 1 (m10443fig1.png)

If we implemented the upsampler/LPF pair with a polyphase filterbank, we would still waste computations due to eventual downsampling by M M. Alternatively, if we implemented the LPF/downsampler pair with a polyphase filterbank, we would waste computations by feeding it the (mostly-zeros) upsampler output. Thus, we need to examine this problem in more detail.

Assume for the moment that we implemented the upsampler/LPF pair with a polyphase filterbank, giving the architecture in Figure 2.

Figure 2
Figure 2 (m10443fig2.png)

Keeping the "parallel-to-serial" interpretation of the upsampler/delay ladder in mind, the input sequence to the decimator ql ql has the form as in Figure 3

Figure 3
Figure 3 (m10443fig2andahalf.png)

leading to the observation that ql= v l L ⌊lL⌋ q l v l L l L

ym=qmM= v m M L ⌊mML⌋=∑k h m M L kx⌊mML⌋-k y m q m M v m M L m M L k k h m M L k x m M L k (1)

Thus, to calculate the resampled output at output index mm, we should calculate only the output of branch number mMmodL m M L at input index ⌊mML⌋m ML. No other branch outputs are calculated, so that no computations are wasted. The resulting structure is depicted in Figure 4.

Figure 4:
Figure 4 (m10443fig3.png)

An equally-efficient structure could be obtained if we implemented the LPF/downsampler using the MM-branch polyphase decimator which was fed with the proper sequence of input samples. However, this structure is not as elegant: rather than computing the output of one particular polyphase branch per output sample, we would need to add all branch outputs, but where each branch output was calculated using a particular subset of polyphase taps.

Comments, questions, feedback, criticisms?

Send feedback