[BUG] - Technical Audit: Fix numerical instabilities for IIR filters

[elybrand]

This PR addresses issue #193 for the filt submodule. Specifically, the following modifications have been made:

1. Update function call in fir.py for firwin(). We now feed in the sampling rate directly, rather than feeding in the deprecated argument nyq, or the nyquist frequency.
2. Previously a warning was raised if you asked for a IIR butterworth filter that was anything but a bandpass. That warning has now been removed.
3. Most importantly, I made changes to how IIR filters are now computed. Instead of computing a and b coefficients of the transfer function, we now compute the second order series expansion. This addresses numerical instabilities for butterworth filters of higher orders. I did not want to change any of the checks or utils for FIR filters, so I created new functions for IIR filters by prepending "sos_" to the function handles. I updated doc strings in all of the functions which referenced a and b values for IIR filters. Finally, I updated the test test_apply_iir_filter to take as input a second order series expansion rather than two arrays of a and b coefficients. TL;DR: IIR filters and related functions now exclusively use second order series representations. FIR filters and related functions are left untouched. This addresses numerical instabilities.

[ryanhammonds]

Hi @elybrand, I had minor comments about adding tests for the new sos funcs, and moving shared code between check_filter_properties and sos_check_filter_properties to a separate func so it's not duplicated. We'll also need to update the api.rst so the new sos funcs are rendered by sphinx for the neurodsp site. I can directly push these changes to this PR if you don't mind?

[elybrand]

@ryanhammonds I am more than okay if you'd like to push those changes to the PR directly.

[TomDonoghue]

Thanks @ericlybrand for the updates here.

Of the updates, 1 & 2 look great! For 3, the update looks great for the technical fix, and I have direct pushed a refactor of how this gets organized into the code.

Tagging back in for review:

• @elybrand : please have a look through the new code, and check that the way coefficients are now handled makes sense / looks good, and I that haven't mangled any of the technical aspects here.
• @ryanhammonds : please review the code overall. I did not do any work to extend the tests to explicitly check & cover the new aspects of managing filter coefs - so please review overall, and then add a commit to add test coverage (I'm assuming we need something added here).

[TomDonoghue]

Closing and re-opening to check a settings thing.

[ryanhammonds]

Everything looks good here! I have updated tests and increased coverage a bit.

[elybrand]

Everything looks good to me.

[TomDonoghue]

Alright, go team! This all looks good to me, so I'm merging in!