Signal Reconstruction from Mel-spectrogram Based on Bi-level Consistency of Full-band Magnitude and Phase

We propose an optimization-based method for reconstructing a time-domain signal from a low-dimensional spectral representation such as a mel-spectrogram. Phase reconstruction has been studied to reconstruct a time-domain signal from the full-band short-time Fourier transform (STFT) magnitude. The Griffin-Lim algorithm (GLA) has been widely used because it relies only on the redundancy of STFT and is applicable to various audio signals. In this paper, we jointly reconstruct the full-band magnitude and phase by considering the bi-level relationships among the time-domain signal, its STFT coefficients, and its mel-spectrogram. The proposed method is formulated as a rigorous optimization problem and estimates the full-band magnitude based on the criterion used in GLA. Our experiments demonstrate the effectiveness of the proposed method on speech, music, and environmental signals.Comment: Accepted to IEEE WASPAA 202

Speckle interferometry

We have presented the basic mathematical treatment of interferometry in the optical domain. Its applications in astronomical observations using both the single aperture, as well as the diluted apertures are described in detail. We have also described about the shortcomings of this technique in the presence of Earth's atmosphere. A short descriptions of the atmospheric turbulence and its effect on the flat wavefront from a stellar source is given. The formation of speckle which acts as carrier of information is defined. Laboratory experiments with phase modulation screens, as well as the resultant intensity distributions due to point source are demonstrated. The experimental method to freeze the speckles, as well as data processing techniques for both Fourier modulus and Fourier phase are described. We have also discussed the technique of the aperture synthesis using non-redundant aperture masks at the pupil plane of the telescope, emphasizing set on the comparison with speckle interferometry. The various methods of image restoration and their comparisons are also discussed. Finally, we have touched upon certain astrophysical problems which can be tackled with the newly developed speckle interferometer using the 2.34 meter Vainu Bappu Telescope (VBT), situated at the Vainu Bappu Observatory (VBO), Kavalur, India.Comment: 32 pages tex files including figure

Discrete structure of the brain rhythms

Neuronal activity in the brain generates synchronous oscillations of the Local Field Potential (LFP). The traditional analyses of the LFPs are based on decomposing the signal into simpler components, such as sinusoidal harmonics. However, a common drawback of such methods is that the decomposition primitives are usually presumed from the onset, which may bias our understanding of the signal's structure. Here, we introduce an alternative approach that allows an impartial, high resolution, hands-off decomposition of the brain waves into a small number of discrete, frequency-modulated oscillatory processes, which we call oscillons. In particular, we demonstrate that mouse hippocampal LFP contain a single oscillon that occupies the $\theta$-frequency band and a couple of $\gamma$-oscillons that correspond, respectively, to slow and fast $\gamma$-waves. Since the oscillons were identified empirically, they may represent the actual, physical structure of synchronous oscillations in neuronal ensembles, whereas Fourier-defined "brain waves" are nothing but poorly resolved oscillons.Comment: 17 pages, 9 figure

Speckle from phase ordering systems

The statistical properties of coherent radiation scattered from phase-ordering materials are studied in detail using large-scale computer simulations and analytic arguments. Specifically, we consider a two-dimensional model with a nonconserved, scalar order parameter (Model A), quenched through an order-disorder transition into the two-phase regime. For such systems it is well established that the standard scaling hypothesis applies, consequently the average scattering intensity at wavevector _k and time t' is proportional to a scaling function which depends only on a rescaled time, t ~ |_k|^2 t'. We find that the simulated intensities are exponentially distributed, with the time-dependent average well approximated using a scaling function due to Ohta, Jasnow, and Kawasaki. Considering fluctuations around the average behavior, we find that the covariance of the scattering intensity for a single wavevector at two different times is proportional to a scaling function with natural variables mt = |t_1 - t_2| and pt = (t_1 + t_2)/2. In the asymptotic large-pt limit this scaling function depends only on z = mt / pt^(1/2). For small values of z, the scaling function is quadratic, corresponding to highly persistent behavior of the intensity fluctuations. We empirically establish a connection between the intensity covariance and the two-time, two-point correlation function of the order parameter. This connection allows sensitive testing, either experimental or numerical, of existing theories for two-time correlations in systems undergoing order-disorder phase transitions. Comparison between theory and our numerical results requires no adjustable parameters.Comment: 18 pgs RevTeX, to appear in PR