On the Designing of Spikes Band-Pass Filters for FPGA

In this paper we present two implementations of spike-based bandpass filters, which are able to reject out-of-band frequency components in the spike domain. First one is based on the use of previously designed spike-based low-pass filters. With this architecture the quality factor, Q, is lower than 0.5. The second implementation is inspired in the analog multi-feedback filters (MFB) topology, it provides a higher than 1 Q factor, and ideally tends to infinite. These filters have been written in VHLD, and synthesized for FPGA. Two spike-based band-pass filters presented take advantages of the spike rate coded representation to perform a massively parallel processing without complex hardware units, like floating point arithmetic units, or a large memory. These low requirements of hardware allow the integration of a high number of filters inside a FPGA, allowing to process several spike coded signals fully in parallel.Ministerio de Ciencia e Innovación TEC2009-10639-C04-0

On the structure of the essential spectrum of elliptic operators on metric spaces

We give a description of the essential spectrum of a large class of operators on metric measure spaces in terms of their localizations at infinity. These operators are analogues of the elliptic operators on Euclidean spaces and our main result concerns the ideal structure of the $C^*$-algebra generated by them.Comment: Improved presentation, some new results

Finite Embeddability of Sets and Ultrafilters

A set A of natural numbers is finitely embeddable in another such set B if every finite subset of A has a rightward translate that is a subset of B. This notion of finite embeddability arose in combinatorial number theory, but in this paper we study it in its own right. We also study a related notion of finite embeddability of ultrafilters on the natural numbers. Among other results, we obtain connections between finite embeddability and the algebraic and topological structure of the Stone-Cech compactification of the discrete space of natural numbers. We also obtain connections with nonstandard models of arithmetic.Comment: to appear in Bulletin of the Polish Academy of Sciences, Math Serie

Dimension reduction for systems with slow relaxation

We develop reduced, stochastic models for high dimensional, dissipative dynamical systems that relax very slowly to equilibrium and can encode long term memory. We present a variety of empirical and first principles approaches for model reduction, and build a mathematical framework for analyzing the reduced models. We introduce the notions of universal and asymptotic filters to characterize `optimal' model reductions for sloppy linear models. We illustrate our methods by applying them to the practically important problem of modeling evaporation in oil spills.Comment: 48 Pages, 13 figures. Paper dedicated to the memory of Leo Kadanof

Building Blocks for Spikes Signals Processing

Neuromorphic engineers study models and implementations of systems that mimic neurons behavior in the brain. Neuro-inspired systems commonly use spikes to represent information. This representation has several advantages: its robustness to noise thanks to repetition, its continuous and analog information representation using digital pulses, its capacity of pre-processing during transmission time, ... , Furthermore, spikes is an efficient way, found by nature, to codify, transmit and process information. In this paper we propose, design, and analyze neuro-inspired building blocks that can perform spike-based analog filters used in signal processing. We present a VHDL implementation for FPGA. Presented building blocks take advantages of the spike rate coded representation to perform a massively parallel processing without complex hardware units, like floating point arithmetic units, or a large memory. Those low requirements of hardware allow the integration of a high number of blocks inside a FPGA, allowing to process fully in parallel several spikes coded signals.Junta de Andalucía P06-TIC-O1417Ministerio de Ciencia e Innovación TEC2009-10639-C04-02Ministerio de Ciencia e Innovación TEC2006-11730-C03-0

The curvelet transform for image denoising

We describe approximate digital implementations of two new mathematical transforms, namely, the ridgelet transform and the curvelet transform. Our implementations offer exact reconstruction, stability against perturbations, ease of implementation, and low computational complexity. A central tool is Fourier-domain computation of an approximate digital Radon transform. We introduce a very simple interpolation in the Fourier space which takes Cartesian samples and yields samples on a rectopolar grid, which is a pseudo-polar sampling set based on a concentric squares geometry. Despite the crudeness of our interpolation, the visual performance is surprisingly good. Our ridgelet transform applies to the Radon transform a special overcomplete wavelet pyramid whose wavelets have compact support in the frequency domain. Our curvelet transform uses our ridgelet transform as a component step, and implements curvelet subbands using a filter bank of a` trous wavelet filters. Our philosophy throughout is that transforms should be overcomplete, rather than critically sampled. We apply these digital transforms to the denoising of some standard images embedded in white noise. In the tests reported here, simple thresholding of the curvelet coefficients is very competitive with "state of the art" techniques based on wavelets, including thresholding of decimated or undecimated wavelet transforms and also including tree-based Bayesian posterior mean methods. Moreover, the curvelet reconstructions exhibit higher perceptual quality than wavelet-based reconstructions, offering visually sharper images and, in particular, higher quality recovery of edges and of faint linear and curvilinear features. Existing theory for curvelet and ridgelet transforms suggests that these new approaches can outperform wavelet methods in certain image reconstruction problems. The empirical results reported here are in encouraging agreement

Perceptually smooth timbral guides by state-space analysis of phase-vocoder parameters

Sculptor is a phase-vocoder-based package of programs that allows users to explore timbral manipulation of sound in real time. It is the product of a research program seeking ultimately to perform gestural capture by analysis of the sound a performer makes using a conventional instrument. Since the phase-vocoder output is of high dimensionality — typically more than 1,000 channels per analysis frame—mapping phase-vocoder output to appropriate input parameters for a synthesizer is only feasible in theory