% Toolbox for the Design of Complex Filters % Copyright (C) 2018 Kenneth Martin

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UPDATE: Dec./2018 This toolbox has undergone a major revision which is on-going. Many many bugs in the filter approximation routines have been fixed and at the time of up-load almost all of the examples in ./examples are working. Numerical conditioning has been significantly improved (this is ongoing). A large number of filter realization functions have been added to ./lib. Again, the update is ongoing and not yet finished. For example, many of the library routines have been deprecated and should be deleted and/or renamed. The intention is this will occur in the next few months. Also, much of the code requires a lot of cleaning, refractoring, more documentation, etc. Again, it is hoped this will occur, and given that currently work on the toolbox is only being done by myself, part-time, it might take a bit of time. The following of this README has not been changed since 2016, but will be updated soon. Good luck, and I hope you enjoy doing complex filter design; it is an area I personally find fascinating even though it doesn't seem to be currently popular. I'm hoping that after finishing the update, I can change directions to looking into using the toolbox in some applications; one area I'm very interested in is maximally decimated filter-banks using IIR digital filters. I've played around in this previously using FIR filters, but I don't think much has been done wrt to IIR filters, and I'm hoping the toolox might be of some use for this application. The examples now include some first efforts at digital filter banks based on cascade filters (for example, see: examples/FltrBnk_1_6_0.m. -Ken

To see some examples of designing filters, start Matlab (Copyright, 1984-2016, The Mathworks Inc.), change directory into ./examples, add ../lib to your path using

path('../lib',path) and then either run the file design_examples.m, or run any of the individual exmpl?.m files

The programs in ./lib are intended for designing transfer functions for complex filters, both analog and digital. The filters can have a single passband, and upper and lower stopbands that need not be symetrical. The programs are highly based on the approach of Martin Snelgrove (see his unpublished paper in ./doc). The programs and approach are described in greater detail in my 12 year old paper also in ./doc (unfortunately, not well proofed; this is on my to-do list). The programs were written in 2004, with a couple of bug fixes recently (mostly a fix for Matlab not well supporting complex models and an extension to handle two fixed adjacent poles). It appears to me (in 2016) that the equivalent routines have not become available in the intervening 12 years, so the routines are being made publically available under the GPLv3 license. The routines do have bugs, and when found, if you could e-mail me at martin@granitesemi.com, I will fix them as I find time. This may take awhile, as complex filter design is currently not my day job; sending suggestions and/or code to fix the bugs will speed up the process. Despite the bugs, the programs do seem to be highly accurate for most of the design examples.

Some suggestions for extensions (perhaps for interested graduate students looking for a thesis topic) are:

1. extend to allow for multiple passbands (perhaps using N-path filters? Franks, L. E. , and I. W. Sandberg, "An Alternative Approach to the Realization of Network Transfer Function: The N-Path Filter. Journal, September 1960. The Bell System Technical)

2. Extend so digital filters are designed directly without using the bilinear transform. I'm hoping to some day get to this using an LDI like approach where the design is done using zp = z^(1/2) - z^(-1/2) as the frequency variable, and then at the end transforming back to the normal z^(-1) variable; maybe you could beat me to it?

3. Extend so phase equalization is included.

4. Fix the Matlab (Copyright, 1984-2016, The Mathworks Inc.) model toolboxes to properly handle complex coefficients.

5. Extend to the muliple-in multiple-out case (this would be really interesting but could be difficult).

6. Extend to adaptive filters where the poles are automatically moved to reject interferers while the exact design of the passbands are preserved; I don't think this would be too difficult for say one or two poles, and could be real useful for wireless front ends. Basically having the filter approximations routines running in the background during actual system operation could take advantage of cheap (Beaglebone Black?) computers. This type of approach (and others like it) strikes me as a whole new methodology that was not previously available

Just some thoughts; I do find playing with Matlab (Copyright, 1984-2016, The Mathworks Inc.) and complex filters to be an enjoyable passtime; perhaps you'll find this to be true as well.

-Ken Martin, originally 2004, then 2016, now 2018.