Very simple RMS based frequency estimator

fvc.py

# References:
#
# 1) Simple and Accurate Frequency to Voltage Converter
#    https://web.mit.edu/Magic/Public/papers/05491499.pdf
#
# 2) Recursive RMS (STM32 Implementation)
#    https://www.youtube.com/watch?v=miUXBXUDJDI
#
# 3) How do I take the discrete derivative of Cosine, and show that it still equals -Sine?
#    https://math.stackexchange.com/a/2276816


import matplotlib.pyplot as plot
import numpy as np


def rms(x, l):

	lx = np.resize(np.pad(x, (l, 0)), x.shape)
	dx = (x**2 - lx**2) / l

	y = np.cumsum(dx)
	y = np.sqrt(y)

	return y


sr = 44100
n  = sr//2
l  = 1000

t = np.arange(n) / sr
f = np.array([100, 200, 400])
a = np.array([1,   1/2, 1/4])

roi = np.min(f) - 100, np.max(f) + 100

x = np.mean(a[:, None] * np.sin(2 * np.pi * f[:, None] * t), axis=0)
y = np.diff(x, prepend=0)

x = rms(x, l)
y = rms(y, l)

with np.errstate(all='ignore'):
	w = y / x
	f = w * sr / (2 * np.pi)

print(np.median(f[~np.isnan(f)]))

plot.plot(t * 1e3, f)
plot.xlabel('ms')
plot.ylabel('hz')
plot.ylim(roi)
plot.show()