with Φ ∈ RN×M , M ≥ N , and some noise . The challenge is to determine the sparsest representation of reconstruction coefficients w = [w1, . . . , wM ] . Finding a sparse representation of a signal in an overcomplete dictionary is equivalent to solving a regularized linear inverse. For a given dictionary Φ, finding the maximally sparse w is an NP-hard problem [1]. A great deal of recent researc...

Signal decomposition is a classical problem in signal processing, which aims to separate an observed signal into two or more components each with its own property. Usually each component is described by its own subspace or dictionary. Extensive research has been done for the case where the components are additive, but in real world applications, the components are often non-additive. For exampl...

Owing to the properties of joint time-frequency analysis that compress energy and approximately decorrelate temporal redundancies in sequential data, filterbank and wavelets are popular and convenient platforms for statistical signal modeling. Motivated by the prior knowledge and empirical studies, much of the emphasis in signal processing has been placed on the choice of the prior distribution...

Electrocardiogram (ECG) signal enhancement and QRS complex detection is a critical preprocessing step for further heart disease analysis and diagnosis. In this paper, we propose a sparse representation-based ECG signal enhancement and QRS complex detection algorithm. Unlike traditional Fourier or wavelet transform-based methods, which use fixed bases, the proposed algorithm models the ECG signa...

Introduction 1 Background 1 Digital Communication Systems 2 Baseband Signal Representation 2 Line Codes 3 Passband Signal Representation 3 Constellation Diagrams 4 Generation of Coherent PSK Signals 4 Representation of BPSK 4 Generation of BPSK 5 Representation and Generation of QPSK 5 M-ary PSK 7 Demodulation of Coherent PSK Signals 8 Spectral Characteristics of PSK Signals 9 Error Performance...

In this paper we compare the effectiveness of rhythm based signal segmentation technique with the traditional fixed length segmentation for music contents representation. We consider vocal regions, instrumental regions and chords which represent the harmony as different class of music contents to be represented. The effectiveness of segmentation for music content representation is measured base...

Harmonic analysis has been the longest lasting and most powerful tool for dealing with signals and systems which involve both periodic and transient phenomena. Further impact on signal processing was facilitated by what we refer to as representations in combined spaces. These representations, motivated by Gabor’s concept of time-frequency information, cells have evolved in recent years into a r...

We present SABR (Sparse, Anchor-Based Representation), an analysis technique to decompose the speech signal into speaker-dependent and speaker-independent components. Given a collection of utterances for a particular speaker, SABR uses the centroid for each phoneme as an acoustic “anchor,” then applies Lasso regularization to represent each speech frame as a sparse non-negative combination of t...

This paper investigates the Signal-to-Noise Ratio (SNR) performance of the Logarithmic Number System (LNS) representation against the SNR performance of the fixed-point representation. Analytic formulas are presented for the evaluation and the comparison of the two aforementioned representations, and the superiority of the LNS representation is demonstrated. It is shown that the base b of the l...

The short-time Fourier transform of a discrete-time signal, which is the Fourier transform of a “windowed” version of the signal, is interpreted as a sliding-window spectrum. This sliding-window spectrum is a function of two variables: a discrete time index, which represents the position of the window, and a continuous frequency variable. It is shown that the signal can be reconstructed from th...