Cascade Polyphase Channelizers Green Technology, Reduced Workload DSP (otherwise known as DSP Magic)
Fredric J. Harris, PhD
University of California San Diego
Recently someone posted a question on a DSP blog I occasionally visit: “How does one design a very narrow bandwidth stopband filter?” As I recall there was a 10 kHz wide stopband, a 5 kHz wide transition band, and a 1 MHz sample rate. Stopband attenuation >60 dB, passband ripple <0.1 dB. A bad combination: low bandwidth, low transition bandwidth, high sample rate! 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. 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. 300 taps seemed to be about the right number. When I read one suggestion from someone I know 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 and when I stopped at 12, or was it 5 multiplies and adds per input-output sample pair?
This presentation will show how to build narrowband filters with more than an order of magnitude reduction of computational 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 a pair of 1400 tap filters implemented with 100 real multiplies per input – output complex sample?