# Filter length in maximally decimated polyphase channelizer

I would like to know whether there is a condition in selecting the number of channels $$M$$ and filter length $$N$$. As of now I am trying to design a channelizer where the data length $$M$$ is much less than the FIR filter length $$N$$.

Right now I am referring to the paper "High Resolution Spectral Analysis and Signal Segregation Using the Polyphase Channelizer" for this implementation. The paper provides a solution to the problem by stacking the filter coefficients such that the the number of taps per channel will increase (where filter length $$N=M \cdot K$$ and finally the number of filter taps per channel is $$K$$).

Finally, what I understood from the paper is to do an element-wise multiplication with the input data with each of the filter taps of length ($$K$$ in this example) and do an average. I am not sure my understanding is correct. So if someone can give a clarity on the implementation it would be helpful.

• Hi! Is this the paper you're referring to? Commented Feb 9 at 13:30
• Yes @MarcusMüller do you have an idea on what the paper discuss Commented Feb 10 at 1:43

The paper provides a solution to the problem by stacking the filter coefficients such that the the number of taps per channel will increase (where filter length N=M⋅K and finally the number of filter taps per channel is K).

That's not specific to the paper, that's just how polyphase systems generally work: Take a prototype filter of length $$N$$, and deinterleave its input or its output (or both, for rational resamplers). So, I think this will be a pretty steep learning curve to learn from the paper alone!

You'll want some textbook to explain polyphase channelizers as used in the paper. Luckily, one of the authors of that paper basically invented the stuff and wrote a classic text book on it; it's good for your needs! You'll want to read Harris, Fred. Multirate Signal Processing for Communication Systems; I think the 2004 version is cheap on the used book market. There, you need chapters 1, 2, 3.1 and 6, and you'll get the theory (and quite a bit of practice) of understanding and designing polyphase channelizers.

Finally, what I understood from the paper is to do an element-wise multiplication with the input data with each of the filter taps of length (K in this example) and do an average

Can't read the paper, but: If that's the case, that's not a polyphase channelizer. You process the input samples in a round-robin fashion through the $$M$$ paths (each of length $$N/K$$) of your polyphase filter; to calculate the $$M$$ output channels, you typically have to add a DFT (in the implementation of an FFT) to the end.

• Hi Marcus, I am bit concerned about the stage just before we perform the FFT. Say for example as per the filter design we are having K taps per channel. Then my concern is if we are going with a maximally decimated filter bank with M number of input samples (where M<<K) how do we perform the round robin operation as you said. Is it like the same input sample can be utilized to multiply all the filter coefficients in the channel or there is some other way we have to address this problem? Commented Feb 12 at 3:31
• Depends; see the book I recommended. In your case, no, in all likelihood, you're not using an input sample for multiple paths. Commented Feb 12 at 9:03
• Ok let me go through the text and will reach out to you if there are any doubts further Commented Feb 12 at 14:51