Green FIR Filters with Large Ratio of Sample Rate to Bandwidth

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. 

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The DSP Biquadratic Recursive Filter: A Fox in the Hen House

When we studied active analog filters we were taught that the biquadratic second order filter was the work horse of active filter design. What made it so was that fact we could form second order polynomials in both denominator and numerator with real coefficients. We also learned that when we performed sensitivity analysis reflecting root shifts with component value variation due to tolerance spreads that lower order polynomials had reduced sensitivity levels. We learned active filters should be implemented with multiple second order filters and possibly one first order filter. Control folks also learned this lesson. That was good perspective for a designer to have.

When we started to implement high order recursive filters in DSP land we followed the standard understanding that the sampled data biquadratic filter with decoupled second order denominator and second order numerators offered us the same capabilities, complex roots with real coefficients and low sensitivity to root shifts due to coefficient quantization. We were so pleased that the carryover from active analog filters to sampled data filters we failed to notice that it was not true! We let the Fox in the Hen house without realizing what we did.

The fox comes out to play when we try to form IIR low-pass filters with a large ratio of sample rate to bandwidth. What we learn is that it just doesn’t work! We need an alternate architecture or we should stop designing recursive filters with very small bandwidths relative to sample rate. One I see all the time is a 30 Hz wide low-pass or high-pass filter running at 48 kHz sample rate. Have you run into that? Did it take long for the hurt to go away when you found out your design didn’t work?  We will discuss how to fix the problem and make the fox go away.

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Live Q&A with fred harris - The DSP Biquadratic Recursive Filter: A Fox in the Hen House

Live Q&A with fred harris following his talk titled "The DSP Biquadratic Recursive Filter: A Fox in the Hen House"

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Live Q&A with fred harris - Green FIR Filters with Large Ratio of Sample Rate to Bandwidth

Live Q&A with fred harris following his talk titled "Green FIR Filters with Large Ratio of Sample Rate to Bandwidth"

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Things We Should Not Do In Future Radios, (Future Designs Should Not Include Past Mistakes) (2020)

Wireless technology is a shining example of a disruptive innovation that has changed society in remarkable ways. The innovation has altered how people communicate, how people access information, how people are entertained, and how people conduct and schedule their social lives. Every human activity advances and grows through a number of influences. One is experience, one is market forces, another is effective education, and yet another is common wisdom. Common wisdom is entrenched perspectives and levels of understanding accepted by the community as guide posts of the process. In fact there are many examples to be found in the wireless community of common wisdom being faulty. Samuel Clemens’ comment “It ain’t what you don’t know that gets you in trouble, it’s what you know for sure that just ain’t so” The wireless community is not free of entrenched faulty common wisdom which is passed on to successive practitioners of the art. Universities are just as liable as industry for not examining and questioning common wisdom. In this presentation we examine the evolution of wireless technology from the early days through now and show how a number of wisdoms can be shown to not be wise but never-the-less have become entrenched in the fabric of our wireless technology

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Multirate Polyphase Filters and Filter Banks, (GREEN Technology, also known as DSP Magic) (2020)

Recently, someone posted a question on a DSP blog I visit occasionally. How does one design a very narrow bandwidth low pass filter? One version of the problem is a filter with 10 Hz wide pass band, a 10 Hz wide transition band, and a 1 kHz sample rate. Stopband attenuation >80 dB with passband ripple <0.01 dB. This a very bad combination: low transition bandwidth with high sample rate! I think students post their homework problems on the blog so I seldom volunteer to do their homework. I did however read the many suggestions posted on the blog submitted by regular subscribers to the blog. They were interesting to read but nothing clever and of limited value. Some were just plain silly, but to quote a famous line, “who am I to judge?” The consensus was that some problems are hard and require lots of resources, this is one of them! All it takes is lots of filter coefficients and lots of multiply and adds. 405 taps seemed to be about the right number. When I read one suggestion from someone I know at Westminster University in London, I simply had to throw my hat in the ring. It then became a game: how small could you make the filter and still satisfy the specifications? For a week I submitted daily solutions requiring fewer and fewer coefficients. I started at 38 M&A per input sample and I stopped when I reached 6 M&A per input sample!

The presentation will show how to build narrowband filters with more than an order of magnitude reduction of workload. The only requirement is that there be a large ratio of sample rate to bandwidth. Once we learn the simple trick to accomplish this reduction we pose the 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 an I-Q filter pair with 1400 taps per arm replaced with a resampling filter requiring only 100 real multiplies?

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Live Q&A Discussion - Multirate Polyphase Filters and Filter Banks, (GREEN Technology, also known as DSP Magic) (2020)

Live Q&A session with fred harris following his talk titled 'Multirate Polyphase Filters and Filter Banks'

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Live Q&A Discussion - Things We Should Not Do In Future Radios (2020)

Live Q&A session with fred harris following his talk titled 'Things We Should Not Do In Future Radios'

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