Log-amplitude Spectra Research Articles

APNet: An All-Frame-Level Neural Vocoder Incorporating Direct Prediction of Amplitude and Phase Spectra

This paper presents a novel neural vocoder named APNet which reconstructs speech waveforms from acoustic features by predicting amplitude and phase spectra directly. The APNet vocoder is composed of an amplitude spectrum predictor (ASP) and a phase spectrum predictor (PSP). The ASP is a residual convolution network which predicts frame-level log amplitude spectra from acoustic features. The PSP also adopts a residual convolution network using acoustic features as input, then passes the output of this network through two parallel linear convolution layers respectively, and finally integrates into a phase calculation formula to estimate frame-level phase spectra. Finally, the outputs of ASP and PSP are combined to reconstruct speech waveforms by inverse short-time Fourier transform (ISTFT). All operations of the ASP and PSP are performed at the frame level. We train the ASP and PSP jointly and define multilevel loss functions based on amplitude mean square error, phase anti-wrapping error, short-time spectral inconsistency error and time domain reconstruction error. Experimental results show that our proposed APNet vocoder achieves an approximately 8x faster inference speed than HiFi-GAN v1 on a CPU due to the all-frame-level operations, while its synthesized speech quality is comparable to HiFi-GAN v1. The synthesized speech quality of the APNet vocoder is also better than that of several equally efficient models. Ablation experiments also confirm that the proposed parallel phase estimation architecture is essential to phase modeling and the proposed loss functions are helpful for improving the synthesized speech quality.

A Neural Vocoder With Hierarchical Generation of Amplitude and Phase Spectra for Statistical Parametric Speech Synthesis

This paper presents a neural vocoder named HiNet which reconstructs speech waveforms from acoustic features by predicting amplitude and phase spectra hierarchically. Different from existing neural vocoders such as WaveNet, SampleRNN and WaveRNN which directly generate waveform samples using single neural networks, the HiNet vocoder is composed of an amplitude spectrum predictor (ASP) and a phase spectrum predictor (PSP). The ASP is a simple DNN model which predicts log amplitude spectra (LAS) from acoustic features. The predicted LAS are sent into the PSP for phase recovery. Considering the issue of phase warping and the difficulty of phase modeling, the PSP is constructed by concatenating a neural source-filter (NSF) waveform generator with a phase extractor. We also introduce generative adversarial networks (GANs) into both ASP and PSP. Finally, the outputs of ASP and PSP are combined to reconstruct speech waveforms by short-time Fourier synthesis. Since there are no autoregressive structures in both predictors, the HiNet vocoder can generate speech waveforms with high efficiency. Objective and subjective experimental results show that our proposed HiNet vocoder achieves better naturalness of reconstructed speech than the conventional STRAIGHT vocoder, a 16-bit WaveNet vocoder using open source implementation and an NSF vocoder with similar complexity to the PSP and obtains similar performance with a 16-bit WaveRNN vocoder. We also find that the performance of HiNet is insensitive to the complexity of the neural waveform generator in PSP to some extend. After simplifying its model structure, the time consumed for generating 1s waveforms of 16kHz speech using a GPU can be further reduced from 0.34s to 0.19s without significant quality degradation.

A history of cepstrum analysis and its application to mechanical problems

It is not widely realised that the first paper on cepstrum analysis was published two years before the FFT algorithm, despite having Tukey as a common author, and its definition was such that it was not reversible even to the log spectrum. After publication of the FFT in 1965, the cepstrum was redefined so as to be reversible to the log spectrum, and shortly afterwards Oppenheim and Schafer defined the “complex cepstrum”, which was reversible to the time domain. They also derived the analytical form of the complex cepstrum of a transfer function in terms of its poles and zeros. The cepstrum had been used in speech analysis for determining voice pitch (by accurately measuring the harmonic spacing), but also for separating the formants (transfer function of the vocal tract) from voiced and unvoiced sources, and this led quite early to similar applications in mechanics. The first was to gear diagnostics (Randall), where the cepstrum greatly simplified the interpretation of the sideband families associated with local faults in gears, and the second was to extraction of diesel engine cylinder pressure signals from acoustic response measurements (Lyon and Ordubadi). Later Polydoros defined the differential cepstrum, which had an analytical form similar to the impulse response function, and Gao and Randall used this and the complex cepstrum in the application of cepstrum analysis to modal analysis of mechanical structures. Antoni proposed the mean differential cepstrum, which gave a smoothed result. The cepstrum can be applied to MIMO systems if at least one SIMO response can be separated, and a number of blind source separation techniques have been proposed for this. Most recently it has been shown that even though it is not possible to apply the complex cepstrum to stationary signals, it is possible to use the real cepstrum to edit their (log) amplitude spectrum, and combine this with the original phase to obtain edited time signals. This has already been used for a wide range of mechanical applications. A very powerful processing tool is an exponential “lifter” (window) applied to the cepstrum, which is shown to extract the modal part of the response (with a small extra damping of each mode corresponding to the window). This can then be used to repress or enhance the modal information in the response according to the application.

Speech analysis-synthesis system using principal components of vowel spectra

We have studied an effective method using principal components spanning a feature space of isolated vowels. A covariance matrix is calculated from many log-amplitude spectra of isolated vowels uttered by a speaker. An eigen equation of the covariance matrix is solved. The resulting eigenvectors are called principal vectors. In the analysis system, log-amplitude spectrum for each frame of a word uttered by the same speaker is transformed to the components on the principal vectors. In the synthesis system, a log-amplitude spectrum is reconstructed using the components on the principal vectors with the largest eigenvalues and the spoken word is synthesized using the LMA filter. We draw the distribution chart of the first and the second principal components extracted from Japanese vowel data. This figure was very similar to the F1—F2 distribution of vowels and so to the vowel classification map in coordinate axes of the degree of constriction and the tongue hump position. The Listening tests showed that the q...

Generative model of spectra for a word using Fujisaki’s model and genetic algorithm

Fujisaki’s model is a generative model of fundamental frequency which approximates original time pattern effectively. In this study, we propose a new generative model of spectral sequence using Fujisaki’s model. We have already proposed a speech synthesis method using vowel space parameters. The vowel space parameter is defined as the component on principal axis obtained by PCA for log-amplitude spectra of isolated vowels. Log-amplitude spectrum can be reconstructed from linear combination of a few principal vectors with coefficients of the vowel space parameters. Using time sequence of the vowel space parameters, we can synthesize a spoken word. In this study, we apply Fujisaki’s model to the time pattern of vowel space parameter. We adopt parameters of Fujisaki’s model as genes of the genetic algorithm. Then, we execute the genetic algorithm with the fitness of similarity between time patterns of Fujisaki’s model and the pattern generated from the vowel space parameter. We obtained synthesized speech which can be recognized as a spoken word at the first generation of the genetic algorithm. As a result of listening test for vowels showed 45 to 80% correct rate at the first generation. Consequently, the effectiveness of the proposed method is shown.

Comparison of 2D and 3D Electromagnetic Approaches to Predict Tropospheric Turbulence Effects in Clear Sky Conditions

Two-dimensional electromagnetic simulations are often used to evaluate the atmospheric turbulence effects on radiowave propagation in clear sky conditions. However, turbulence is clearly a three-dimensional atmospheric process. Therefore, errors potentially introduced by 2D propagation schemes to predict 3D scintillation effects have to be quantitatively assessed. On the one hand, as part of an analytical approach and starting from the Kolmogorov-von Karman turbulent spectrum, 2D formulations for log-amplitude and phase variances and for log-amplitude and phase temporal power spectra are derived from the 2D scalar propagation equation. They are compared asymptotically to their classical 3D counterparts. On the other hand, as part of a numerical approach, the scintillation effects are evaluated from 3D and 2D parabolic wave equation (PWE) approaches associated with 2D and 1D multiple phase screen (MPS), respectively. It is then shown that 2D propagation schemes underestimate by a factor 1.86 the log-amplitude variances in Fresnel regime and can lead to significant errors in predicting log-amplitude and phase temporal spectra at low frequencies. It is then suggested that the dimensional reduction should be limited to the prediction of log-amplitude and phase variances in Fraunhofer configurations, or to the evaluation of log-amplitude and phase power spectra at high frequencies.

Estimating attenuation and the relative information content of amplitude and phase spectra

Seismic attenuation affects both the amplitude and phase of seismic waves. Algorithms to estimate attenuation are split among those that use amplitude information (e.g., spectral-ratio method), those that use phase information (e.g., rise-time method), and those that use a combination of both (e.g., time-domain algorithms). In this study, I explore the relative information provided by amplitude and phase spectra. To do this, I show how the difference in phase spectra between waveforms recorded at two depth levels can be used to estimate attenuation. This phase-difference method is analogous to the method of spectral ratios, but uses phase information rather than amplitude information. Under the simplifying assumption that the noise in both log-amplitude and phase spectra can be modeled as uncorrelated Gaussian random variables with equal variance, the posterior variances in the attenuation estimates from the spectral-ratio and phase-difference methods can be compared directly. It turns out that over typical seismic bandwidths and typical levels of attenuation, the relative uncertainty in estimates of attenuation from phase spectra is approximately twice the relative uncertainty in estimates of attenuation from log-amplitude spectra. Including phase and amplitude information simultaneously (as opposed to just amplitude information) reduces the relative uncertainty by only about 10% over seismic bandwidths. This reduction in uncertainty is not large, but may be significant depending on the sensitivity of the application.

Integrated estimation of interval-attenuation profiles

Quantitative estimates of seismic attenuation are useful for a variety of applications, ranging from seismic-acquisition design, to seismic processing, amplitude analysis, and reservoir characterization. I frame the estimation of interval attenuation from a set of seismic wavelets as a linear inversion of their log-amplitude spectra. The initial spectrum at the first depth location and a set of depth-varying amplitude scalers are estimated simultaneously with an effective-attenuation [Formula: see text] profile. The algorithm can be regarded as a tomographic extension of the spectral-ratio method that uses all the information available in the amplitude spectra, appropriately weighted so that estimates are not biased by noise. Constraints can be applied to ensure the [Formula: see text] values vary smoothly, and solving for log [Formula: see text] rather than [Formula: see text] ensures only positive attenuation values. Tests on synthetic and field data illustrate the trade-off between vertical resolution and sensitivity to noise. A covariance study indicates that improvements in interval-attenuation estimates over the traditional spectral-ratio method come from systematic-noise handling and the explicit constraints on [Formula: see text], rather than the fact that the inversion ties the log-spectral data together with a single estimate of the spectrum at the first depth location.

Path-averaged surface fluxes determined from infrared and microwave scintillometers

Methods are needed to measure the surface fluxes of sensible ( H) and latent heat ( E) at large scales. A promising method is scintillometry. Over pasture, a near-infrared scintillometer was most sensitive to temperature fluctuations whilst a microwave scintillometer was unduly affected by both humidity fluctuations and correlated temperature–humidity fluctuations. Slower changes in path-averaged humidity caused additional signal variance and an overestimation of H and E. Log-amplitude spectra of the microwave scintillometer signal showed inertial-convective subrange behavior. In combination, path-averaged E and H could be determined over 3 km. Independent corroborative measurements of H and E were made at the path midpoint using the eddy covariance technique. For sensible heat, agreement was within 4% over a measured range 0–300 W m −2, with a residual standard deviation of 45 W m −2. Latent heat agreed at best to within 12% over the range 0–450 W m −2 (residual standard deviation of 94 W m −2) and an offset of 30 W m −2.

VHF scintillations as a diagnostic tool for the study of ionospheric irregularities

In this paper we present the results of observations of the scintillations of radio beacon on 250.351 MHz from geostationary satellite FLEETSAT (73° E) recorded at Bombay on April 9–10, 1992 during night hours. The scintillation index,S4, is used to describe the strength of the scintillations. The variation of scintillation index with local time shows a maxima of 0.589 at 02:55 IST. This scintillation activity is linked with the spreadF-irregularities. A brief description of the scintillation theories like phase screen theory and theory for weak scintillations - Rytov solution is given. These theories provide an integral measure of the fluctuations in terms of phase and amplitude fluctuations imposed on VHF signals while traversing through the ionosphere. Power spectrum analysis for the log-amplitude and phase departure and cross spectrum between them have also been carried out. Using spectral indexp = 1, we have shown that the scale sizes for the ionospheric irregularities are greater than 1 km.

Acoustic propagation and oceanic fine structure.

Internal waves distort the sound-speed field in the sea. This time variable distortion causes fluctuations in acoustic intensity and phase in forward transmission experiments. Initial efforts to predict the spectrum of internal wave-induced phase fluctuations were successful. Corresponding success was not achieved in the prediction of acoustic intensity, which is sensitive to smaller vertical scales than phase. Are the oceanic environmental models inaccurate or are the relevant scattering models in error? Here, a statistical picture of the fine-scale wave field is presented. The data consist of 10 000 profiles of density and sound speed, from the sea surface to 560 m, collected over a 20-day period. Vertical wave-number-frequency spectra of sound-speed anomaly are estimated from these profiles. Of relevance is the frequency dependence of the spectrum at the vertical wave number corresponding to the Fresnel scale of a given acoustic experiment. In an Eulerian frame, where vertical advection influences the observations, the frequency dependence varies significantly with vertical wave number. The form, as well as level, of the power spectrum of log intensity is dependent on the Fresnel scale of the experiment. Since estimation of the Fresnel scale is sometimes associated with significant uncertainty, the shape of the log amplitude spectrum might prove a valuable guide to the scattering physics.

Frequency spectra of acoustic fluctuations caused by oceanic internal waves and other finestructure

The frequency spectrum of log-amplitude fluctuations is substantially modified (flattened) by a previously neglected effect: the vertical advection of short internal waves by the more energetic internal waves with large vertical wavelength. The log-amplitude spectrum is sensitive to this vertical advection and to curvature of the equilibrium sound ray, whereas the phase spectrum is not. Noninternal-wave ’’frozen’’ finestructure contributes to the log-amplitude frequency spectrum through vertical advection, but not to the phase spectrum. The Cobb Seamount experiment is treated as an example; the spectrum of the modified theory agrees well with observations except at high frequency ( near the buoyancy frequency ).

Estimation of turbulence spectra parameters from log-amplitude fluctuations spectra of an optical wave

From the general formula for the temporal frequency log-amplitude fluctuations spectra the asymptotic expressions are found, valid for the geometric and wave approximations. A comparison of the plane and spherical wave formulas with those valid for the beam wave is made in all frequency regions. The difference between the on-axis and off-axis beam spectra is presented. The possibility of estimating from the log-amplitude scintillations the inner and outer scales of turbulence together with the exponent of turbulence spectra in the subrange is briefly discussed.

Source shape estimation and deconvolution of teleseismic bodywaves

We consider the deconvolution of a suite of teleseismic recordings of the same event in order to separate source and transmission path phenomena. The assumption of source uniformity may restrict the range of muths and distances of the seismograms included in the suite. The source shape is estimated by separately averaging the log amplitude spectra and the phase spectra of the recordings. This method of source estimation uses the redundant source information contained in secondary arrivals. The necessary condition for this estimator to resolve the source wavelet is that the travel times of the various secondary arrivals be evenly distributed with respect to the initial arrivals. The subsequent deconvolution of the seismograms is carried out by spectral division with two modifications. The first is the introduction of a minimum allowable source spectral amplitude termed the waterlevel. This parameter constrains the gain of the deconvolution filter in regions where the seismogram has little or no information, and also trades-off arrival time resolution with arrival amplitude resolution. The second modification, designed to increase the time domain resolution of the deconvolution, is the extension of the frequency range of the transmission path impulse response spectrum beyond the optimal passband (the passband of the seismograms). The justification for the extension lies in the fact that the impulse response of the transmission path is itself a series of impulses which means its spectrum is not band-limited. Thus, the impulse response is best represented by a continuous spectrum rather than one which is set to zero outside the optimal passband. This continuity is achieved by a recursive application of a unit-step prediction operator determined by Burg's maximum entropy algorithm. The envelopes of the deconvolution are used to detect the presence of phase shifted arrivals.

Newer concepts of the pitch, the loudness and the timbre of musical tones

It is not widely realised that the first paper on cepstrum analysis was published two years before the FFT algorithm, despite having Tukey as a common author, and its definition was such that it was not reversible even to the log spectrum. After publication of the FFT in 1965, the cepstrum was redefined so as to be reversible to the log spectrum, and shortly afterwards Oppenheim and Schafer defined the “complex cepstrum”, which was reversible to the time domain. They also derived the analytical form of the complex cepstrum of a transfer function in terms of its poles and zeros. The cepstrum had been used in speech analysis for determining voice pitch (by accurately measuring the harmonic spacing), but also for separating the formants (transfer function of the vocal tract) from voiced and unvoiced sources, and this led quite early to similar applications in mechanics. The first was to gear diagnostics (Randall), where the cepstrum greatly simplified the interpretation of the sideband families associated with local faults in gears, and the second was to extraction of diesel engine cylinder pressure signals from acoustic response measurements (Lyon and Ordubadi). Later Polydoros defined the differential cepstrum, which had an analytical form similar to the impulse response function, and Gao and Randall used this and the complex cepstrum in the application of cepstrum analysis to modal analysis of mechanical structures. Antoni proposed the mean differential cepstrum, which gave a smoothed result. The cepstrum can be applied to MIMO systems if at least one SIMO response can be separated, and a number of blind source separation techniques have been proposed for this. Most recently it has been shown that even though it is not possible to apply the complex cepstrum to stationary signals, it is possible to use the real cepstrum to edit their (log) amplitude spectrum, and combine this with the original phase to obtain edited time signals. This has already been used for a wide range of mechanical applications. A very powerful processing tool is an exponential “lifter” (window) applied to the cepstrum, which is shown to extract the modal part of the response (with a small extra damping of each mode corresponding to the window). This can then be used to repress or enhance the modal information in the response according to the application.