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[Undescribed Horrific Abuse, One Victim & Survivor of Many]

Here's what I have right now for fftfreq. I'm excited to have factored
fftfreq out and added optional minimum and maximum frequency bounds.
The rest of fourier.py is 1 email back.

This interface does not facilitate the usecase of having minimum and
maximum frequency bounds and simply desiring as many freq_count and
freq_sample_rate as makes sense with the bounds.

Thinking: the purpose of freq_sample_rate was to test against data
that had been generated at sampled at a specific different rate, and
was occurring in a larger recording. But maybe it would be more
appropriate to consolidate that information into freq_count, min_freq,
and max_freq, given in real recordings there is usually only one time
base.

# AGPL-3 Karl Semich 2022
import numpy as np

def fftfreq(freq_count, sample_rate = None, min_freq = None, max_freq
= None, dc_offset = True, freq_sample_rate = None):
    if sample_rate is None and freq_sample_rate is None:
        sample_rate = 1
        freq_sample_rate = 1
    elif sample_rate is None:
        sample_rate = freq_sample_rate
    elif freq_sample_rate is None:
        freq_sample_rate = sample_rate
    if not dc_offset:
        freq_count += 1
    if min_freq is None:
        min_freq = freq_sample_rate / freq_count
    min_freq /= sample_rate
    if freq_count % 2 == 0:
        if max_freq is None:
            max_freq = freq_sample_rate / 2
        max_freq /= sample_rate
        neg_freqs = np.linspace(-max_freq, -min_freq,
num=freq_count//2, endpoint=True)
        pos_freqs = -neg_freqs[:0:-1]
    else:
        if max_freq is None:
            max_freq = freq_sample_rate * (freq_count - 1) / 2 / freq_count
        max_freq /= sample_rate
        pos_freqs = np.linspace(min_freq, max_freq, num=freq_count//2,
endpoint=True)
        neg_freqs = -pos_freqs[::-1]
    return np.concatenate([
        np.array([0] if dc_offset else []),
        pos_freqs,
        neg_freqs
    ])

def peak_pair_idcs(freq_data):
    freq_heights = abs(freq_data) # squares and sums the components
    paired_heights = freq_height[...,1:-1] + freq_height[...,2:]
    peak_idx = paired_heights.argmax(axis=-1, keepdims=True) + 1
    return np.concatenate(peak_idx, peak_idx + 1, axis=-1)