def freq_from_hps(signal, fs):
"""Estimate frequency using harmonic product spectrum
Low frequency noise piles up and overwhelms the desired peaks
"""
N = len(signal)
signal -= mean(signal) # Remove DC offset
# Compute Fourier transform of windowed signal
windowed = signal * kaiser(N, 100)
# Get spectrum
X = log(abs(rfft(windowed)))
# Downsample sum logs of spectra instead of multiplying
hps = copy(X)
for h in 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 = argmax(hps[:len(dec)])
i_interp = parabolic(hps, i_peak)[0]
# Convert to equivalent frequency
return fs * i_interp / N # Hz
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 find fundamental for inharmonic things like
musical instruments, this implementation has trouble with finding the true
peak
"""
# Calculate autocorrelation (same thing as convolution, but with one input
# reversed in time), and throw away the negative lags
signal -= mean(signal) # Remove DC offset
corr = fftconvolve(signal, signal[::-1], mode='full')
corr = corr[len(corr)/2:]
# Find the first low point
d = 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 = argmax(corr[start:]) + start
i_interp = parabolic(corr, i_peak)[0]
return fs / i_interp
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
"""
# Calculate autocorrelation (same thing as convolution, but with one input
# reversed in time), and throw away the negative lags
signal -= mean(signal) # Remove DC offset
corr = fftconvolve(signal, signal[::-1], mode='full')
corr = corr[len(corr)/2:]
# Find the first low point
d = 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 = argmax(corr[start:]) + start
i_interp = parabolic(corr, i_peak)[0]
return fs / i_interp
def freq_from_hps(signal, fs):
"""Estimate frequency using harmonic product spectrum
Low frequency noise piles up and overwhelms the desired peaks
"""
N = len(signal)
signal -= mean(signal) # Remove DC offset
# Compute Fourier transform of windowed signal
windowed = signal * kaiser(N, 100)
# Get spectrum
X = log(abs(rfft(windowed)))
# Remove mean of spectrum (so sum is not increasingly offset
# only in overlap region)
X -= mean(X)
# Downsample sum logs of spectra instead of multiplying
hps = copy(X)
for h in arange(2, 9): # TODO: choose a smarter upper limit
h = int(h) # https://github.com/scipy/scipy/pull/7351
dec = decimate(X, h, zero_phase=True)
hps[:len(dec)] += dec
# Find the peak and interpolate to get a more accurate peak
i_peak = argmax(hps[:len(dec)])
i_interp = parabolic(hps, i_peak)[0]
# Convert to equivalent frequency
return fs * i_interp / N # Hz
def THD(signal, sample_rate):
"""Measure the THD for a signal
This function is not yet trustworthy.
Returns the estimated fundamental frequency and the measured THD,
calculated by finding peaks in the spectrum.
There are two definitions for THD, a power ratio or an amplitude ratio
When finished, this will list both
"""
# Get rid of DC and window the signal
signal -= mean(signal) # TODO: Do this in the frequency domain, and take any skirts with it?
windowed = signal * kaiser(len(signal), 100)
# Find the peak of the frequency spectrum (fundamental frequency)
f = rfft(windowed)
i = argmax(abs(f))
true_i = parabolic(log(abs(f)), i)[0]
print 'Frequency: %f Hz' % (sample_rate * (true_i / len(windowed)))
print 'fundamental amplitude: %.3f' % abs(f[i])
# Find the values for the first 15 harmonics. Includes harmonic peaks only, by definition
# TODO: Should peak-find near each one, not just assume that fundamental was perfectly estimated.
# Instead of limited to 15, figure out how many fit based on f0 and sampling rate and report this "4 harmonics" and list the strength of each
for x in range(2, 15):
print '%.3f' % abs(f[i * x]),
THD = sum([abs(f[i*x]) for x in range(2,15)]) / abs(f[i])
print '\nTHD: %f%%' % (THD * 100)
return
def freq_from_hps(signal, fs):
"""Estimate frequency using harmonic product spectrum
Low frequency noise piles up and overwhelms the desired peaks
"""
N = len(signal)
signal -= mean(signal) # Remove DC offset
# Compute Fourier transform of windowed signal
windowed = signal * kaiser(N, 100)
# Get spectrum
X = log(abs(rfft(windowed, _next_regular(N))))
# Downsample sum logs of spectra instead of multiplying
hps = copy(X)
for h in 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 = argmax(hps[:len(dec)])
i_interp = parabolic(hps, i_peak)[0]
# Convert to equivalent frequency
return fs * i_interp / N # Hz
def freq_from_fft(sig, fs):
# Compute Fourier transform of windowed signal
windowed = sig * blackmanharris(len(sig))
fe = rfft(windowed)
# Find the peak and interpolate to get a more accurate peak
i = argmax(abs(fe)) # Just use this for less-accurate, naive version
true_i = parabolic(log(abs(fe)), i)[0]
# Convert to equivalent frequency
return fs * true_i / len(windowed)
def THDN(signal, sample_rate):
"""Measure the THD+N for a signal and print the results
Prints the estimated fundamental frequency and the measured THD+N. This is
calculated from the ratio of the entire signal before and after
notch-filtering.
This notch-filters by nulling out the frequency coefficients ±10% of the
fundamental
"""
# Get rid of DC and window the signal
signal -= mean(
signal
) # TODO: Do this in the frequency domain, and take any skirts with it?
windowed = signal * kaiser(len(signal), 100)
del signal
# Zero pad to nearest power of two
new_len = 2**ceil(log(len(windowed)) / log(2))
windowed = concatenate((windowed, zeros(new_len - len(windowed))))
# Measure the total signal before filtering but after windowing
total_rms = rms_flat(windowed)
# Find the peak of the frequency spectrum (fundamental frequency)
f = rfft(windowed)
i = argmax(abs(f))
true_i = parabolic(log(abs(f)), i)[0]
print 'Frequency: %f Hz' % (sample_rate * (true_i / len(windowed)))
# Filter out fundamental by throwing away values ±10%
lowermin = true_i - 0.1 * true_i
uppermin = true_i + 0.1 * true_i
f[lowermin:uppermin] = 0
# Transform noise back into the time domain and measure it
noise = irfft(f)
THDN = rms_flat(noise) / total_rms
# TODO: RMS and A-weighting in frequency domain?
# Apply A-weighting to residual noise (Not normally used for distortion,
# but used to measure dynamic range with -60 dBFS signal, for instance)
weighted = A_weight(noise, sample_rate)
THDNA = rms_flat(weighted) / total_rms
print "THD+N: %.4f%% or %.1f dB" % (THDN * 100, 20 * log10(THDN))
print "A-weighted: %.4f%% or %.1f dB(A)" % (THDNA * 100, 20 * log10(THDNA))
def THDN(signal, sample_rate):
"""Measure the THD+N for a signal and print the results
Prints the estimated fundamental frequency and the measured THD+N. This is
calculated from the ratio of the entire signal before and after
notch-filtering.
This notch-filters by nulling out the frequency coefficients ±10% of the
fundamental
"""
# Get rid of DC and window the signal
signal -= mean(signal) # TODO: Do this in the frequency domain, and take any skirts with it?
windowed = signal * kaiser(len(signal), 100)
del signal
# Zero pad to nearest power of two
new_len = 2**ceil( log(len(windowed)) / log(2) )
windowed = concatenate((windowed, zeros(new_len - len(windowed))))
# Measure the total signal before filtering but after windowing
total_rms = rms_flat(windowed)
# Find the peak of the frequency spectrum (fundamental frequency)
f = rfft(windowed)
i = argmax(abs(f))
true_i = parabolic(log(abs(f)), i)[0]
print 'Frequency: %f Hz' % (sample_rate * (true_i / len(windowed)))
# Filter out fundamental by throwing away values ±10%
lowermin = true_i - 0.1 * true_i
uppermin = true_i + 0.1 * true_i
f[lowermin: uppermin] = 0
# Transform noise back into the time domain and measure it
noise = irfft(f)
THDN = rms_flat(noise) / total_rms
# TODO: RMS and A-weighting in frequency domain?
# Apply A-weighting to residual noise (Not normally used for distortion,
# but used to measure dynamic range with -60 dBFS signal, for instance)
weighted = A_weight(noise, sample_rate)
THDNA = rms_flat(weighted) / total_rms
print "THD+N: %.4f%% or %.1f dB" % (THDN * 100, 20 * log10(THDN))
print "A-weighted: %.4f%% or %.1f dB(A)" % (THDNA * 100, 20 * log10(THDNA))
def freq_from_fft(signal, fs):
"""Estimate frequency from peak of FFT
Pros: Accurate, usually even more so than zero crossing counter
(1000.000004 Hz for 1000 Hz, for instance). Due to parabolic
interpolation being a very good fit for windowed log FFT peaks?
https://ccrma.stanford.edu/~jos/sasp/Quadratic_Interpolation_Spectral_Peaks.html
Accuracy also increases with signal length
Cons: Doesn't find the right value if harmonics are stronger than
fundamental, which is common.
"""
N = len(signal)
# Compute Fourier transform of windowed signal
windowed = signal * kaiser(N, 100)
f = rfft(windowed)
# Find the peak and interpolate to get a more accurate peak
i_peak = argmax(abs(f)) # Just use this value for less-accurate result
i_interp = parabolic(log(abs(f)), i_peak)[0]
# Convert to equivalent frequency
return fs * i_interp / N # Hz
def freq_from_fft(signal, fs):
"""Estimate frequency from peak of FFT
Pros: Accurate, usually even more so than zero crossing counter
(1000.000004 Hz for 1000 Hz, for instance). Due to parabolic
interpolation being a very good fit for windowed log FFT peaks?
https://ccrma.stanford.edu/~jos/sasp/Quadratic_Interpolation_Spectral_Peaks.html
Accuracy also increases with signal length
Cons: Doesn't find the right value if harmonics are stronger than
fundamental, which is common.
"""
N = len(signal)
# Compute Fourier transform of windowed signal
windowed = signal * kaiser(N, 100)
f = rfft(windowed)
# Find the peak and interpolate to get a more accurate peak
i_peak = argmax(abs(f)) # Just use this value for less-accurate result
i_interp = parabolic(log(abs(f)), i_peak)[0]
# Convert to equivalent frequency
return fs * i_interp / N # Hz
