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Polyphase Analysis and Synthesis Filter banks: capabilities and implementation

Fredric J Harris - Watch Now - Duration: 03:01:25

Polyphase Analysis and Synthesis Filter banks: capabilities and implementation
Fredric J Harris

Two papers related to this workshop and made available by fred harris:

Polyphase Analysis and Synthesis filter banks, a very important segment of the multirate signal processing community, are the most incredible signal processing algorithms. Your first reaction to your understanding them is: “I’ll be darned!” Your second reaction is: “I can hardly wait to tell all my friends about this!” Do you know about these things?

Let’s start with the analysis filter bank which has a dual structure called the synthesis filter bank. Each does the opposite of the other. The analysis channelizer processes a sampled data input signal spanning a wide frequency band containing many contiguous narrow bandwidth channels. The result of that processing is a set of narrow bandwidth signals translated from their original centers to baseband and low-pass filtered to their channel bandwidths to separate them from their neighbors and further down sampled to a rate commensurate with their reduced bandwidths. This process for a single channel is called a digital down converter (DDC). The remarkable property of the analysis channelizer is the cost of M (say 100) channels is only about the cost of 5 channels. Amazingly the process occurs in a completely different manner and order of what you would imagine! Rather than down convert, filter, and reduce sample rate, the sample rate is reduced on the way into the filter bank and the processing is performed at the reduced output rate instead at the high input rate. 

If we were a fly on the wall we might overhear this conversation between a potential buyer and the salesperson in the polyphase analysis filter bank store. The customer asks “What will a single channel DDC cost me?” The salesperson answers “It will cost you $10”. The customer then asks “What will 10 equal BW channels of DDCs cost me?” The salesperson answers “it will cost you $100 but if you are interested, we have a special this week; we have a 100 channel DDC for only $50. For that price, you can compute all 100 channels, throw away 90 of them and still have your 10 channels at a reduced price!” Which option do you think the customer will buy?  Have we caught your attention? 

There is surely another store in town that sells synthesis filter banks. These banks up sample many baseband narrowband signals a higher sample rate and translates the baseband signals to selected center frequencies to form a composite broadband spectrum. These are digital up converters (DUCs).  The two filter banks are duals of each other; one uses aliasing caused by down sampling to translate all the band center signals to baseband and a clever trick to separate the aliases while the other uses aliasing caused by up-sampling to translate all the baseband signals to selected band centers and the same trick to perform the dual task of separating the up-sampled aliased spectral bands.

We will review the signal processing sequence of the M-path analysis and synthesis channelizers. We will then go through all the steps to implement the MATLAB realizations of the same and illustrate performance and methods of verifying its operation. This is a process you have to do three or four times till it finally clicks. I have former students contact me and ask “Remind me why we did this thing at this point in the script?” Reset time!

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