Multirate Polyphase Filters and Filter Banks, (GREEN Technology, also known as DSP Magic)
Fredric J Harris - Watch Now
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?