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## Green FIR Filters with Large Ratio of Sample Rate to Bandwidth

Fredric J Harris - **Watch Now** - Duration: 01:27:51

This presentation will show you how to design and implement narrowband filters with more than an order of magnitude reduction of workload. I was recently challenged to reduce the workload for a 301 tap low pass FIR filter with sample rate 50 times the bandwidth. After my first approach in which I reduced the workload to 21 multiplies I wondered by how much could we reduce the workload? I finally stopped playing with the question when I reached 6 multiplies, which is a 50-to-1 workload reduction. The technique we present usually reduces the workload by a factor greater than 10. The only requirement to apply these techniques is that there be a large ratio of sample rate to bandwidth. Once we learn the simple trick to accomplish this reduction we then pose the next question: can we achieve similar reduction in workload when there is not a large ratio of sample rate to bandwidth? The answer surprisingly is yes? We will share the recipe for the secret sauce so you too will know how wideband filters can also be implement with more than an order of magnitude workload reduction. How about a pair of 1400 complex tap filters replaced with 100 real multiplies?

When I first started showing folks how to build FIR filters with an order of magnitude workload reduction, no-one seemed interested in clever solutions. I realized I had a marketing blind spot. I fixed that blind spot and now tell folks let me show you a green solution to your problem! There is hardly any room left on the bandwagon.

**fred_h**Speaker

**adam.rex**

I would be interested in the code for an M-path linear phase IIR filter bank.

**Amit**

Prof. Harris,

would it be possible to get the code for the M-Path Linear phase IIR filter bank

thanks

**adam.rex**

Can polyphase FIR filter design reduce delay compared to a non-polyphase FIR filter?

**remco_at_itsonlyaudio.com**

Boy did you bury the lead in the last few minutes!

So for a log spaced polyphase bank, do you keep the transition bandwidths equal to assure the 6 dB Nyquist overlap but scale the bandwidths by the square root multiplier? Wouldn't that lead to a varying number of coefficients for each polyphase bank?

**magarac**

thank you so much for great presentation dr harris ! I'm curious to learn more about polyphase filterbank for hearing aids which is topic of your upcoming paper, but did not catch when/where will it be published. also, some specifics about inband aliasing that might affect some processing like echo-canceller, etc...

thanks & best regards !

**Stefano**

Hi Fred,

It is always an immense pleasure listening to your talks.

Regarding RF direct sampling, what are your thoughts about one analog Hilbert transformer followed by 2 ADCs, rather than directly sampling RF with one ADC? With the first approach we would have the 2 ADCs running at half speed but never seen a system done in this way so far.

Thanks!

Stefano

adam,

The polyphase filter that implements a cascade of analysis and binary masked synthesis filter bank always has a longer delay that the direct FIR filter implementation... because you have gone through two filters between input and output....

What is interesting, there is a recursive form of the polyphase filter, one with non uniform phase and one form with linear phase (actually equal ripple approximation to linear phase) the linear phase version will present a reduced delay relative to the direct form FIR.... see my book and if interested... I can pass along the code for the M-Path Linear phase IIR filter bank...