[ENH] - Add IRASA

[TomDonoghue]

Add an implementation of IRASA.

Note - this implementation is inspired by / draws from the one in YASA:
https://github.com/raphaelvallat/yasa/blob/master/yasa/spectral.py#L326

Reviews / ToDos:

• @elybrand : if you feel like you have a sense of IRASA, can you check the implementation for technical sound-ness?
  • also, I wanted to add the implementation so you can play with it. Feel free to 'explore' it for a while before proper reviewing
• @ryanhammonds : can you check the code elements & double check it is well organized to fit into NDSP
  • so far, there are no tests, so if you could add some code tests that would be great!
• @rdgao : tagging you in since you've played with IRASA a bit - but nothing in particular needed!
  • thought you might be interested in checking it out / sanity checking the implementation!

Some quickstart code to try it (it seems to work in the simple case):

from neurodsp.aperiodic.irasa import *

from neurodsp.sim import sim_combined
from neurodsp.spectral import compute_spectrum, trim_spectrum
from neurodsp.plts import plot_power_spectra

n_seconds, fs = 10, 1000
sim_components = {'sim_powerlaw': {'exponent' : -2},
                  'sim_oscillation': {'freq' : 10}}
sig = sim_combined(n_seconds=n_seconds, fs=fs, components=sim_components)
f1, p1 = trim_spectrum(*compute_spectrum(sig, fs), [1, 30])

freqs, psd_ap, psd_pe = irasa(sig, fs, noverlap=int(2*fs))
b0, b1 = fit_irasa(freqs, psd_ap)

print('Estimated intercept & slope: {:1.3f}, {:1.3f}'.format(b0, b1))
plot_power_spectra([f1, freqs], [p1, psd_ap], labels=['Original', 'IRASA-AP'])

Creates this output:

[ryanhammonds]

@TomDonoghue Everything here looks good to me. I pushed tests updates.

[elybrand]

EDIT: there was a bug in my spline code.

So I was going to suggest following what Wen and Liu do for upsampling and downsampling, which is to use cubic splines to interpolate. I decided to try and implement this to compare against what is currently done using scipy.signal.resample_poly which filters and then imputes with zeroes. I was a bit surprised to find that the cubic spline method basically performs identically to the current way of upsampling and downsampling. I benchmarked on sum of sinusoids models with various central frequencies and the two methods differed very slightly but imperceptibly so. I did notice some interesting behavior with IRASA but I'll post that in an issue.

Anyways, I think what's currently implemented is good.

[TomDonoghue]

Okay, this all looks sounds good to me!

@elybrand - thanks for the dive into the resampling! I was curious about the resampling approach here, and glad to see the different approaches seem equivalent! This is a a really nice sanity check to have.
@ryanhammonds - thanks for adding the tests! I mildly updated organization, if you want to sanity check that!

Some notes for myself:
This should be merged after #167. After that PR is merged, rebase here, and revisit for conflicts and check / update here for test signals updates; aperiodic init file; API listing, then this can also be merged.

[ryanhammonds]

@TomDonoghue I went though your updates and everything looks good to me.

[TomDonoghue]

This all seems good then - merging in!