""" 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