Update acf <-> psd conversions

[ryanhammonds]

Addresses #29 and updates the conversion functions. For ACF -> PSD:

import matplotlib.pyplot as plt
import numpy as np
from neurodsp.spectral import compute_spectrum
from statsmodels.tsa.stattools import acf
from timescales.sim import sim_exp_decay, sim_ar
from timescales.conversions import acf_to_psd, psd_to_acf

# Parameters
fs = 1000
phi = 0.95

# Target ACF
tau = -1/(np.log(phi) * fs)
lags = np.arange(5000)
corrs = sim_exp_decay(lags, fs, tau, 1.)

# Simulated sample
sig = sim_ar(1000, 1000, np.array([phi]))

# ACF to PSD
freqs, powers = acf_to_psd(corrs, fs)
freqs_welch, powers_welch = compute_spectrum(sig, fs, nperseg=5001)

plt.loglog(freqs_welch[1:], powers_welch[1:] / powers_welch[:20].mean(), label='Welch, from simulated signal')
plt.loglog(freqs[1:], powers[1:] / powers[1], label='abs(iff(acf(t)))^2, from theoretical acf')
plt.legend()

For PSD -> ACF:

# AR(1) PSD
freqs = np.linspace(0.01, fs//2, 20000)
powers = 1 / (1 - 2 * phi * np.cos(2 * np.pi * freqs * 1/fs) + phi**2)

# Convert PSD to ACF
lags_ifft, corrs_ifft = psd_to_acf(freqs, powers, fs)

plt.plot(lags[:100], corrs[:100], label='simulated acf')
plt.plot(lags_ifft[:50], corrs_ifft[:50], label='ifft(powers), from simulate AR(1) psd', ls='--')

These fft conversions agree on the PSD forms from on the AR(1) PSD (#31 has spectral fitting for AR(p)), and OU and AR(1) simulations. This deviates from the Lorentzian form in specparam. The specparam form can be derived from the AR(1) PSD using a couple approximations, e.g. taylor approximation of the cosine term above. These approximations result in bias as the knee frequency increases towards nyquist.