Frame Theory for Signal Processing in Psychoacoustics

This review chapter aims to strengthen the link between frame theory and signal processing tasks in psychoacoustics. On the one side, the basic concepts of frame theory are presented and some proofs are provided to explain those concepts in some detail. The goal is to reveal to hearing scientists how this mathematical theory could be relevant for their research. In particular, we focus on frame theory in a filter bank approach, which is probably the most relevant view-point for audio signal processing. On the other side, basic psychoacoustic concepts are presented to stimulate mathematicians to apply their knowledge in this field

Texture Segmentation Using Gabor Filters and Wavelets

The present work deals with image segmentation which results in the subdivision of an image into its constituent regions or objects. The result of image segmentation is a set of segments that collectively cover the entire image or a set of contours extracted from the image. Each of the pixels in a region are similar with respect to some characteristic or computed property, such as color, intensity or texture. Specifically this project deals with texture segmentation of an image to find out the different types of textures present in the image. In this project different type of procedures have been followed to carry out texture segmentation. Procedures starting from fundamental filter transforms till multi-resolution technique using wavelet transform have been considered. Many texture-segmentation schemes are based on a filter-bank model, where the filters called Gabor filters are derived from Gabor elementary functions. Both linear and circular Gabor filters are studied and analyzed in this aspect and how these filters are better in comparison to linear filters is also analyzed. Different types of wavelet transform techniques like Haar transform, S transform, etc. are followed and their performance regarding texture segmentation is being studied

A biomimetic basis for auditory processing and the perception of natural sounds

Biomimicry is a powerful science that aims to take advantage of nature's remarkable ability to devise innovative solutions to challenging problems. In the setting of hearing, mimicking how humans hear is the foremost strategy in designing effective artificial hearing approaches. In this work, we explore the mathematical foundations for the exchange of design inspiration and features between biological hearing systems, artificial sound-filtering devices, and signal processing algorithms. Our starting point is a concise asymptotic analysis of subwavelength acoustic metamaterials. We are able to fine tune this structure to mimic the biomechanical properties of the cochlea, at the same scale. We then turn our attention to developing a biomimetic signal processing algorithm. We use the response of the cochlea-like structure as an initial filtering layer and then add additional biomimetic processing stages, designed to mimic the human auditory system's ability to recognise the global properties of natural sounds

Stability properties of periodically driven overdamped pendula and their implications to physics of semiconductor superlattices and Josephson junctions

We consider the first order differential equation with a sinusoidal nonlinearity and periodic time dependence, that is, the periodically driven overdamped pendulum. The problem is studied in the case that the explicit time-dependence has symmetries common to pure ac-driven systems. The only bifurcation that exists in the system is a degenerate pitchfork bifurcation, which describes an exchange of stability between two symmetric nonlinear modes. Using a type of Prufer transform to a pair of linear differential equations, we derive an approximate condition of the bifurcation. This approximation is in very good agreement with our numerical data. In particular, it works well in the limit of large drive amplitudes and low external frequencies. We demonstrate the usefulness of the theory applying it to the models of pure ac-driven semiconductor superlattices and Josephson junctions. We show how the knowledge of bifurcations in the overdamped pendulum model can be utilized to describe effects of rectification and amplification of electric fields in these microstructures.Comment: 15 pages, 7 figures, Revtex 4.1. Revised and expanded following referee's report. Submitted to journal Chaos

A property of the elementary symmetric functions”,

Abstract In this paper, a relation between the elementary symmetric functions on the frequencies of multi-sine wave signal and its multiple integrals is proposed. In particular, such relation is useful to obtain a closed-form expression for the frequencies estimation. The approach used herein is based on the algebraic derivative method in the frequency domain, which allows to yield exact formula in terms of multiple integrals of the signal when placed in the time domain. Moreover, it allows to free oneself from the hypothesis of uniform sampling. Two different ways to approach the estimation are advised, the first is based on least-squares estimation, while the second one is based on the solution of a linear system of dimension equal to the number of sinusoidal components involved. For an easy time realization of such formula, a time-varying filter is proposed. Due to use of multiple integrals of the signal, the resulting parameters estimation is accurate in the face of large measurement noise. To corroborate the theoretical analysis and to investigate the performance of the developed algorithm, computer simulated and laboratory experiments data records are processed

Kramers-Kronig, Bode, and the meaning of zero

The implications of causality, as captured by the Kramers-Kronig relations between the real and imaginary parts of a linear response function, are familiar parts of the physics curriculum. In 1937, Bode derived a similar relation between the magnitude (response gain) and phase. Although the Kramers-Kronig relations are an equality, Bode's relation is effectively an inequality. This perhaps-surprising difference is explained using elementary examples and ultimately traces back to delays in the flow of information within the system formed by the physical object and measurement apparatus.Comment: 8 pages; American Journal of Physics, to appea