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DSP Lecture 15 Multirate signal processing and polyphase representations
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ECSE-4530 Digital Signal Processing • Rich Radke, Rensselaer Polytechnic Institute • Lecture 15: Multirate signal processing and polyphase representations (10/23/14) • 0:00:01 Recap of downsampling and upsampling by integer factors • 0:02:15 Frequency-domain sketches • 0:04:49 Review of prefiltering • 0:08:22 Changing the sampling rate by a non-integer factor • 0:09:10 Rational factors: upsampling by an integer and downsampling by another integer • 0:12:29 Combining the middle low-pass filters • 0:15:22 Not a great idea if the intermediate rate changes are needlessly large • 0:18:04 The Noble identities • 0:18:12 Switching the order of downsampling and filtering • 0:27:11 Switching the order of upsampling and filtering • 0:30:26 Polyphase decomposition of a filter • 0:31:24 Time-domain subsequences • 0:36:25 Polyphase components of a filter • 0:37:52 Block diagram of polyphase decomposition/reconstruction • 0:40:37 The completed polyphase diagram • 0:41:45 Chained-delay polyphase structure • 0:43:38 The completed chain-delay polyphase diagram • 0:45:35 Z-transform interpretation of polyphase • 0:48:42 Polyphase realization of transfer function • 0:50:08 Efficient decimation/interpolation using polyphase decompositions • 0:50:49 Polyphase decimation • 0:54:21 Applying the Noble identity for efficiency • 0:58:20 Polyphase interpolation • 1:00:46 Applying the Noble identity for efficiency • Follows Sections 10.4-10.5 of the textbook (Proakis and Manolakis, 4th ed.).
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