def freq_from_autocorr(signal, fs):
"""
Estimate frequency using autocorrelation.
Pros: Best method for finding the true fundamental of any repeating wave,
even with strong harmonics or completely missing fundamental
Cons: Not as accurate, doesn't work for inharmonic things like musical
instruments, this implementation has trouble with finding the true peak
From: https://gist.github.com/endolith/255291 and
https://github.com/endolith/waveform-analyzer
Parameters
----------
signal : list or array
time series data
fs : integer
sample rate
Returns
-------
frequency : float
frequency (Hz)
"""
import numpy as np
from scipy.signal import fftconvolve
from matplotlib.mlab import find
from mhealthx.signals import parabolic
# Calculate autocorrelation (same thing as convolution, but with one input
# reversed in time), and throw away the negative lags:
signal -= np.mean(signal) # Remove DC offset
corr = fftconvolve(signal, signal[::-1], mode='full')
corr = corr[len(corr)/2:]
# Find the first low point:
d = np.diff(corr)
start = find(d > 0)[0]
# Find the next peak after the low point (other than 0 lag). This bit is
# not reliable for long signals, due to the desired peak occurring between
# samples, and other peaks appearing higher.
i_peak = np.argmax(corr[start:]) + start
i_interp = parabolic(corr, i_peak)[0]
frequency = fs / i_interp
return frequency
def freq_from_hps(signal, fs):
"""
Estimate frequency using harmonic product spectrum.
Note: Low frequency noise piles up and overwhelms the desired peaks.
From: https://gist.github.com/endolith/255291 and
https://github.com/endolith/waveform-analyzer
Parameters
----------
signal : list or array
time series data
fs : integer
sample rate
Returns
-------
frequency : float
frequency (Hz)
"""
import numpy as np
from scipy.signal import blackmanharris, decimate
from mhealthx.signals import parabolic
N = len(signal)
signal -= np.mean(signal) # Remove DC offset
# Compute Fourier transform of windowed signal:
windowed = signal * blackmanharris(len(signal))
# Get spectrum:
X = np.log(abs(np.fft.rfft(windowed)))
# Downsample sum logs of spectra instead of multiplying:
hps = np.copy(X)
for h in np.arange(2, 9): # TODO: choose a smarter upper limit
dec = decimate(X, h)
hps[:len(dec)] += dec
# Find the peak and interpolate to get a more accurate peak:
i_peak = np.argmax(hps[:len(dec)])
i_interp = parabolic(hps, i_peak)[0]
# Convert to equivalent frequency:
frequency = fs * i_interp / N # Hz
return frequency
