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"""
Functions for analyzing vocal characteristics: jitter, shimmer, HNR, and GNE.
These are typically used for analysis of dysarthric voices using more traditional approaches
(i.e. not deep learning). Often useful as a baseline for e.g. pathology detection. Inspired by PRAAT.
Authors
* Peter Plantinga, 2024
"""
import torch
import torchaudio
PERIODIC_NEIGHBORS = 4
@torch.no_grad()
def compute_autocorr_features(frames, min_lag, max_lag, neighbors=5):
"""Compute features based on autocorrelation
Arguments
---------
frames: torch.Tensor
The audio frames to be evaluated for autocorrelation, shape [batch, frame, sample]
min_lag: int
The minimum number of samples to consider for potential period length.
max_lag: int
The maximum number of samples to consider for potential period length.
neighbors: int
The number of neighbors to use for rolling median -- to avoid octave errors.
Returns
-------
harmonicity: torch.Tensor
The highest autocorrelation score relative to the 0-lag score. Used to compute HNR
best_lags: torch.Tensor
The lag corresponding to the highest autocorrelation score, an estimate of period length.
Example
-------
>>> audio = torch.rand(1, 16000)
>>> frames = audio.unfold(-1, 800, 200)
>>> frames.shape
torch.Size([1, 77, 800])
>>> harmonicity, best_lags = compute_autocorr_features(frames, 100, 200)
>>> harmonicity.shape
torch.Size([1, 77])
>>> best_lags.shape
torch.Size([1, 77])
"""
autocorrelation = autocorrelate(frames)
# Find the peak, lag
harmonicity, lags = autocorrelation[:, :, min_lag:max_lag].max(dim=-1)
# Take median value of 5 neighboring cells to avoid octave errors
lags = torch.nn.functional.pad(lags, pad=(2, 2))
best_lags, _ = lags.unfold(-1, neighbors, 1).median(dim=-1)
# Re-add the min_lag back in after first step removed it
best_lags = best_lags + min_lag
return harmonicity, best_lags
def autocorrelate(frames):
"""Generate autocorrelation scores using circular convolution.
Arguments
---------
frames: torch.Tensor
The audio frames to be evaluated for autocorrelation, shape [batch, frame, sample]
Returns
-------
autocorrelation: torch.Tensor
The ratio of the best candidate lag's autocorrelation score against
the theoretical maximum autocorrelation score at lag 0.
Normalized by the autocorrelation_score of the window.
Example
-------
>>> audio = torch.rand(1, 16000)
>>> frames = audio.unfold(-1, 800, 200)
>>> frames.shape
torch.Size([1, 77, 800])
>>> autocorrelation = autocorrelate(frames)
>>> autocorrelation.shape
torch.Size([1, 77, 401])
"""
# Apply hann window to the audio to reduce edge effects
window_size = frames.size(-1)
hann = torch.hann_window(window_size, device=frames.device).view(1, 1, -1)
autocorrelation = compute_cross_correlation(frames * hann, frames * hann)
# Score should be normalized by the autocorrelation of the window
# See 'Accurate Short-Term Analysis of the Fundamental Frequency
# and the Harmonics-To-Noise Ratio of a Sampled Sound' by Boersma
norm_score = compute_cross_correlation(hann, hann).clamp(min=1e-10)
return autocorrelation / norm_score
@torch.no_grad()
def compute_periodic_features(frames, best_lags, neighbors=PERIODIC_NEIGHBORS):
"""Function to compute periodic features: jitter, shimmer
Arguments
---------
frames: torch.Tensor
The framed audio to use for feature computation, dims [batch, frame, sample].
best_lags: torch.Tensor
The estimated period length for each frame, dims [batch, frame].
neighbors: int
Number of neighbors to use in comparison.
Returns
-------
jitter: torch.Tensor
The average absolute deviation in period over the frame.
shimmer: torch.Tensor
The average absolute deviation in amplitude over the frame.
Example
-------
>>> audio = torch.rand(1, 16000)
>>> frames = audio.unfold(-1, 800, 200)
>>> frames.shape
torch.Size([1, 77, 800])
>>> harmonicity, best_lags = compute_autocorr_features(frames, 100, 200)
>>> jitter, shimmer = compute_periodic_features(frames, best_lags)
>>> jitter.shape
torch.Size([1, 77])
>>> shimmer.shape
torch.Size([1, 77])
"""
# Prepare for masking
masked_frames = torch.clone(frames).detach()
mask_indices = torch.arange(frames.size(-1), device=frames.device)
mask_indices = mask_indices.view(1, 1, -1).expand(frames.shape)
periods = best_lags.unsqueeze(-1)
period_indices = mask_indices.remainder(periods)
# Mask everything not within about 20% (1/5) of a period peak
jitter_range = periods // 5
peak, lag = torch.max(masked_frames, dim=-1, keepdim=True)
# Handle lags close to period by checking +-1 period
lag_indices = lag.remainder(periods)
mask = (period_indices < lag_indices - jitter_range) & (
period_indices > lag_indices - periods + jitter_range
) | (period_indices > lag_indices + jitter_range) & (
period_indices < lag_indices + periods - jitter_range
)
masked_frames[mask] = 0
# Find neighboring peaks
peaks, lags = [], []
for i in range(neighbors):
peak, lag = torch.max(masked_frames, dim=-1, keepdim=True)
mask = (mask_indices > lag - periods // 2) & (
mask_indices < lag + periods // 2
)
masked_frames[mask] = 0
peaks.append(peak.squeeze(-1))
lags.append(lag.squeeze(-1))
peaks = torch.stack(peaks, dim=-1)
lags = torch.stack(lags, dim=-1)
# Jitter = average variation in period length
# Compute mean difference from mean lag, normalized by period
lags = lags.remainder(periods)
lags = torch.minimum(lags, periods - lags)
jitter_frames = (lags - lags.float().mean(dim=-1, keepdims=True)).abs()
jitter = jitter_frames.mean(dim=-1) / best_lags
# Shimmer = average variation in amplitude
# Computed as mean difference from mean amplitude, normalized by avg amplitude
avg_amps = peaks.mean(dim=-1, keepdims=True)
amp_diff = (peaks - avg_amps).abs()
shimmer = amp_diff.mean(dim=-1) / avg_amps.squeeze(-1).clamp(min=1e-10)
return jitter, shimmer
@torch.no_grad()
def compute_spectral_features(spectrum, eps=1e-10):
"""Compute statistical measures on spectral frames
such as flux, skew, spread, flatness.
Reference page for computing values:
https://www.mathworks.com/help/audio/ug/spectral-descriptors.html
Arguments
---------
spectrum: torch.Tensor
The spectrum to use for feature computation, dims [batch, frame, freq].
eps: float
A small value to avoid division by 0.
Returns
-------
features: torch.Tensor
A [batch, frame, 8] tensor of spectral features for each frame:
* centroid: The mean of the spectrum.
* spread: The stdev of the spectrum.
* skew: The spectral balance.
* kurtosis: The spectral tailedness.
* entropy: The peakiness of the spectrum.
* flatness: The ratio of geometric mean to arithmetic mean.
* crest: The ratio of spectral maximum to arithmetic mean.
* flux: The average delta-squared between one spectral value and it's successor.
Example
-------
>>> audio = torch.rand(1, 16000)
>>> window_size = 800
>>> frames = audio.unfold(-1, window_size, 200)
>>> frames.shape
torch.Size([1, 77, 800])
>>> hann = torch.hann_window(window_size).view(1, 1, -1)
>>> windowed_frames = frames * hann
>>> spectrum = torch.abs(torch.fft.rfft(windowed_frames))
>>> spectral_features = compute_spectral_features(spectrum)
>>> spectral_features.shape
torch.Size([1, 77, 8])
"""
# To keep features in a neural-network-friendly range, use normalized freq [0, 1]
nfreq = spectrum.size(-1)
freqs = torch.linspace(0, 1, nfreq, device=spectrum.device).view(1, 1, -1)
# Mean, spread, skew, kurtosis. 1-4th standardized moments
centroid = spec_norm(freqs, spectrum).unsqueeze(-1)
spread = spec_norm((freqs - centroid) ** 2, spectrum).sqrt()
skew = spec_norm((freqs - centroid) ** 3, spectrum) / (spread**3 + eps)
kurt = spec_norm((freqs - centroid) ** 4, spectrum) / (spread**4 + eps)
centroid = centroid.squeeze(-1)
# Entropy measures the peakiness of the spectrum
entropy = -(spectrum * (spectrum + eps).log()).mean(dim=-1)
# Flatness is ratio of geometric to arithmetic means
# Use a formulation of geometric mean that is numerically stable
geomean = (spectrum + eps).log().mean(-1).exp()
flatness = geomean / (spectrum.mean(dim=-1) + eps)
# Crest measures the ratio of maximum to sum
crest = spectrum.amax(dim=-1) / (spectrum.sum(dim=-1) + eps)
# Flux is the root-mean-square deltas, padded to maintain same shape
pad = spectrum[:, 0:1, :]
flux = torch.diff(spectrum, dim=1, prepend=pad).pow(2).mean(dim=-1).sqrt()
return torch.stack(
(centroid, spread, skew, kurt, entropy, flatness, crest, flux), dim=-1
)
def spec_norm(value, spectrum, eps=1e-10):
"""Normalize the given value by the spectrum."""
return (value * spectrum).sum(dim=-1) / (spectrum.sum(dim=-1) + eps)
@torch.no_grad()
def compute_gne(
audio,
sample_rate=16000,
bandwidth=1000,
fshift=300,
frame_len=0.03,
hop_len=0.01,
):
"""An algorithm for GNE computation from the original paper:
"Glottal-to-Noise Excitation Ratio - a New Measure for Describing
Pathological Voices" by D. Michaelis, T. Oramss, and H. W. Strube.
This algorithm divides the signal into frequency bands, and compares
the correlation between the bands. High correlation indicates a
relatively low amount of noise in the signal, whereas lower correlation
could be a sign of pathology in the vocal signal.
Godino-Llorente et al. in "The Effectiveness of the Glottal to Noise
Excitation Ratio for the Screening of Voice Disorders." explore the
goodness of the bandwidth and frequency shift parameters, the defaults
here are the ones recommended in that work.
Arguments
---------
audio : torch.Tensor
The batched audio signal to use for GNE computation, [batch, sample]
sample_rate : float
The sample rate of the input audio.
bandwidth : float
The width of the frequency bands used for computing correlation.
fshift : float
The shift between frequency bands used for computing correlation.
frame_len : float
Length of each analysis frame, in seconds.
hop_len : float
Length of time between the start of each analysis frame, in seconds.
Returns
-------
gne : torch.Tensor
The glottal-to-noise-excitation ratio for each frame of the audio signal.
Example
-------
>>> sample_rate = 16000
>>> audio = torch.rand(1, sample_rate) # 1s of audio
>>> gne = compute_gne(audio, sample_rate=sample_rate)
>>> gne.shape
torch.Size([1, 98])
"""
assert audio.dim() == 2, (
"Expected audio to be 2-dimensional, [batch, sample]"
)
# Step 1. Downsample to 10 kHz since voice energy is low above 5 kHz
old_sample_rate, sample_rate = sample_rate, 10000
audio = torchaudio.functional.resample(audio, old_sample_rate, sample_rate)
# Step 2a. Unfold into analysis frames
frame_size = int(sample_rate * frame_len)
hop_size = int(sample_rate * hop_len)
window = torch.hann_window(frame_size, device=audio.device).view(1, 1, -1)
frames = audio.unfold(dimension=-1, size=frame_size, step=hop_size) * window
# Step 2b. Inverse filter each frame with 13th order LPC
excitation_frames = inverse_filter(frames, lpc_order=13)
# Step 3. Compute Hilbert envelopes for each frequency bin
min_freq, max_freq = bandwidth // 2, sample_rate // 2 - bandwidth // 2
center_freqs = range(min_freq, max_freq, fshift)
envelopes = {
center_freq: compute_hilbert_envelopes(
excitation_frames, center_freq, bandwidth, sample_rate
)
for center_freq in center_freqs
}
# Step 4. Compute cross correlation between (non-neighboring) frequency bins
correlations = [
compute_cross_correlation(envelopes[freq_i], envelopes[freq_j], width=3)
for freq_i in center_freqs
for freq_j in center_freqs
if freq_j - freq_i > bandwidth // 2
]
# Step 5. The maximum cross-correlation is the GNE score
return torch.stack(correlations, dim=-1).amax(dim=(2, 3))
def inverse_filter(frames, lpc_order=13):
"""Perform inverse filtering on frames to estimate glottal pulse train.
Uses autocorrelation method and Linear Predictive Coding (LPC).
Algorithm from https://course.ece.cmu.edu/~ece792/handouts/RS_Chap_LPC.pdf
Arguments
---------
frames : torch.Tensor
The audio frames to filter using inverse filter.
lpc_order : int
The size of the filter to compute and use on the frames.
Returns
-------
filtered_frames : torch.Tensor
The frames after the inverse filter is applied
Example
-------
>>> audio = torch.rand(1, 10000)
>>> frames = audio.unfold(-1, 300, 100)
>>> frames.shape
torch.Size([1, 98, 300])
>>> filtered_frames = inverse_filter(frames)
>>> filtered_frames.shape
torch.Size([1, 98, 300])
"""
# Only lpc_order autocorrelation values are needed
autocorrelation = compute_cross_correlation(frames, frames, width=lpc_order)
# Collapse frame and batch into same dimension, for lfiltering
batch, frame_count, _ = autocorrelation.shape
autocorrelation = autocorrelation.view(batch * frame_count, -1)
reshaped_frames = frames.view(batch * frame_count, -1)
# An autocorrelation of all 0's -- which can happen in padding -- leads to
# an error with the linear system solver, as the matrix is singular
# We fix this by ensuring the zero-lag correlation is always 1
autocorrelation[:, lpc_order] = 1.0
# Construct Toeplitz matrices (one per frame)
# This is [[p0, p1, p2...], [p1, p0, p1...], [p2, p1, p0...] ...]
# Our sliding window should go from the end to the front, so flip
# Also, we have one more value on each end than we need, for the target values
R = autocorrelation[:, 1:-1].unfold(-1, lpc_order, 1).flip(dims=(1,))
r = autocorrelation[:, lpc_order + 1 :]
# Solve for LPC coefficients, generate inverse filter with coeffs 1, -b_1, ...
lpc = torch.linalg.solve(R, r)
lpc_coeffs = torch.nn.functional.pad(-lpc, (1, 0), value=1)
a_coeffs = torch.zeros_like(lpc_coeffs)
a_coeffs[:, 0] = 1
# Perform filtering
inverse_filtered = torchaudio.functional.lfilter(
reshaped_frames, a_coeffs, lpc_coeffs, clamp=False
)
# Un-collapse batch and frames
return inverse_filtered.view(batch, frame_count, -1)
def compute_hilbert_envelopes(
frames, center_freq, bandwidth=1000, sample_rate=10000
):
"""Compute the hilbert envelope of the signal in a specific frequency band using FFT.
Arguments
---------
frames : torch.Tensor
A set of frames from a signal for which to compute envelopes.
center_freq : float
The target frequency for the envelope.
bandwidth : float
The size of the band to use for the envelope.
sample_rate : float
The number of samples per second in the frame signals.
Returns
-------
envelopes : torch.Tensor
The computed envelopes.
Example
-------
>>> audio = torch.rand(1, 10000)
>>> frames = audio.unfold(-1, 300, 100)
>>> frames.shape
torch.Size([1, 98, 300])
>>> envelope = compute_hilbert_envelopes(frames, 1000)
>>> envelope.shape
torch.Size([1, 98, 300])
"""
# Step 0. Compute low/high freq for window
low_freq = center_freq - bandwidth / 2
high_freq = center_freq + bandwidth / 2
# Step 1. Compute DFT for each frame
spectra = torch.fft.fft(frames)
freqs = torch.fft.fftfreq(spectra.size(-1), 1 / sample_rate)
# Step 2. Mask with hann window in the frequency range (negative freqs are 0)
mask = torch.zeros_like(spectra, dtype=torch.float)
window_bins = (low_freq < freqs) & (freqs < high_freq)
window = torch.hann_window(window_bins.sum(), device=mask.device)
mask[:, :, window_bins] = window
# Step 3. Apply inverse DFT to get complex time-domain signal
analytic_signal = torch.fft.ifft(spectra * mask)
# Step 4. Take absolute value to get final envelopes
return analytic_signal.abs()
def compute_cross_correlation(frames_a, frames_b, width=None):
"""Computes the correlation between two sets of frames.
Arguments
---------
frames_a : torch.Tensor
frames_b : torch.Tensor
The two sets of frames to compare using cross-correlation,
shape [batch, frame, sample]
width : int, default is None
The number of samples before and after 0 lag. A width of 3 returns 7 results.
If None, 0 lag is put at the front, and the result is 1/2 the original length + 1,
a nice default for autocorrelation as there are no repeated values.
Returns
-------
The cross-correlation between frames_a and frames_b.
Example
-------
>>> frames = torch.arange(10).view(1, 1, -1).float()
>>> compute_cross_correlation(frames, frames, width=3)
tensor([[[0.6316, 0.7193, 0.8421, 1.0000, 0.8421, 0.7193, 0.6316]]])
>>> compute_cross_correlation(frames, frames)
tensor([[[1.0000, 0.8421, 0.7193, 0.6316, 0.5789, 0.5614]]])
"""
# Padding is used to control the number of outputs
batch_size, frame_count, frame_size = frames_a.shape
pad = (0, frame_size // 2) if width is None else (width, width)
padded_frames_a = torch.nn.functional.pad(frames_a, pad, mode="circular")
# Cross-correlation with conv1d, by keeping each frame as its own channel
# The batch and frame channel have to be combined due to conv1d restrictions
merged_size = batch_size * frame_count
reshaped_a = padded_frames_a.view(1, merged_size, -1)
reshaped_b = frames_b.view(merged_size, 1, -1)
cross_correlation = torch.nn.functional.conv1d(
input=reshaped_a, weight=reshaped_b, groups=merged_size
)
# Separate out the batch and frame dimensions again
cross_correlation = cross_correlation.view(batch_size, frame_count, -1)
# Normalize
norm = torch.sqrt((frames_a**2).sum(dim=-1) * (frames_b**2).sum(dim=-1))
cross_correlation /= norm.unsqueeze(-1).clamp(min=1e-10)
return cross_correlation