Results 1  10
of
17
If the Independent Components of Natural Images are Edges, What are the Independent Components of Natural Sounds?
, 2001
"... Previous work has shown that various flavours of Independent Component Analysis, when applied to natural images, all result in broadly similar localised, oriented bandpass feature detectors, which have been likened to wavelets or edge detectors. ..."
Abstract

Cited by 11 (1 self)
 Add to MetaCart
Previous work has shown that various flavours of Independent Component Analysis, when applied to natural images, all result in broadly similar localised, oriented bandpass feature detectors, which have been likened to wavelets or edge detectors.
Recent developments in the theory of the fractional Fourier and linear canonical transforms
, 2004
"... ..."
Covariant TimeFrequency Analysis
, 2002
"... We present a theory of linear and bilinear/quadratic timefrequency (TF) representations that satisfy a covariance property with respect to \TF displacement operators." These operators cause TF displacements such as (possibly dispersive) TF shifts, dilations/compressions, etc. Our covariance ..."
Abstract

Cited by 8 (1 self)
 Add to MetaCart
We present a theory of linear and bilinear/quadratic timefrequency (TF) representations that satisfy a covariance property with respect to \TF displacement operators." These operators cause TF displacements such as (possibly dispersive) TF shifts, dilations/compressions, etc. Our covariance theory establishes a uni ed framework for important classes of linear TF representations (e.g., shorttime Fourier transform and continuous wavelet transform) as well as bilinear TF representations (e.g., Cohen's class and ane class). It yields a theoretical basis for TF analysis and allows the systematic construction of covariant TF representations.
Time–FrequencyBased Detection Using DiscreteTime DiscreteFrequency Wigner Distributions
"... Abstract—During the last decade, a comprehensive theory for optimum time–frequency (TF)based detection has been developed. This was originally proposed in the continuoustime continuousfrequency case. This paper deals with detectors operating on discretetime discretefrequency Wigner distribution ..."
Abstract

Cited by 6 (0 self)
 Add to MetaCart
(Show Context)
Abstract—During the last decade, a comprehensive theory for optimum time–frequency (TF)based detection has been developed. This was originally proposed in the continuoustime continuousfrequency case. This paper deals with detectors operating on discretetime discretefrequency Wigner distributions (WDs). The purpose is to discuss some existing definitions of this distribution within the context of TFbased detection and selecting those that do not affect the performance of the decision device with which they are associated. This question is of interest since there exist several approches for discretizing the WD, sometimes resulting in a loss of fundamental properties. First, the discretetime discretefrequency formulations of optimum detection are investigated. Next, the problem of the design of TFbased detectors from training data, keeping in mind severe effects of the curse of dimensionality, is considered. I.
Sparse Representations with Chirplets via Maximum Likelihood Estimation
"... We formulate the problem of approximating a signal with a sum of chirped Gaussians, the socalled chirplets, under the framework of maximum likelihood estimation. For a signal model of one chirplet in noise, we formulate the maximum likelihood estimator (MLE) and compute the Cram'erRao lower b ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
We formulate the problem of approximating a signal with a sum of chirped Gaussians, the socalled chirplets, under the framework of maximum likelihood estimation. For a signal model of one chirplet in noise, we formulate the maximum likelihood estimator (MLE) and compute the Cram'erRao lower bound. An approximate MLE is developed, based on timefrequency methods, and is applied sequentially to obtain a decomposition of multiple chirplets. The decomposition is refined after each iteration with the expectationmaximization algorithm. A version of the algorithm, which is O(N) for each chirplet of the decomposition, is applied to a data set of whale whistles. I. Introduction Chirplets are a class of signals that consists of Gaussians that are translated in time and frequency, scaled, and chirped. They are defined as s t;!;c;d = s(n; t; !; c; d) = ( p 2d) \Gamma 1 2 exp n \Gamma \Gamma n\Gammat 2d \Delta 2 + j c 2 (n \Gamma t) 2 + j!(n \Gamma t) o : where t, !, and c...
A DISCRETE TIME AND FREQUENCY WIGNERVILLE DISTRIBUTION: PROPERTIES AND IMPLEMENTATION
"... Timefrequency distributions are used in the analysis and processing of nonstationary signals. The WignerVille distribution (WVD) is a fundamental timefrequency distribution uniquely satisfying many desirable mathematical properties. The realisation of this distribution for hardware or software pl ..."
Abstract

Cited by 4 (3 self)
 Add to MetaCart
(Show Context)
Timefrequency distributions are used in the analysis and processing of nonstationary signals. The WignerVille distribution (WVD) is a fundamental timefrequency distribution uniquely satisfying many desirable mathematical properties. The realisation of this distribution for hardware or software platforms requires a discrete version. Historically the majority of the work on deriving discrete versions of the WVD has focused on creating aliasfree distributions, often resulting in a loss of some desirable properties. Here a new discrete time and frequency WVD will be presented for nonperiodic signals and will be examined both in terms of its properties and aliasing. In particular unitarity, an assumed property for optimum timefrequency detection and signal estimation, and invertibility, a useful property especially for timefrequency filtering, will be examined. An efficient implementation of the distribution using standard realvalued fast Fourier transforms will also be presented. 1.
Linear redundancy of information carried by the discrete Wigner distribution
 IEEE Trans. Sig. Proc
"... Abstract—The discrete Wigner distribution (WD) encodes information in a redundant fashion since it derives by representations fromsample signals. The increased amount of data often prohibits its effective use in applications such as signal detection, parameter estimation, and pattern recognition. A ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
(Show Context)
Abstract—The discrete Wigner distribution (WD) encodes information in a redundant fashion since it derives by representations fromsample signals. The increased amount of data often prohibits its effective use in applications such as signal detection, parameter estimation, and pattern recognition. As a consequence, it is of great interest to study the redundancy of information it carries. Recently, Richard and Lengellé have shown that linear relations connect the time–frequency samples of the discrete WD. However, up until now, such a redundancy has still not been algebraically characterized. In this paper, the problem of the redundancy of information carried by the discrete cross WD of complexvalued signals is addressed. We show that every discrete WD can be fully recovered from a small number of its samples via a linear map. The analytical expression of this linear map is derived. Special cases of the auto WD of complexvalued signals and realvalued signals are considered. The results are illustrated by means of computer simulations, and some extensions are pointed out. Index Terms—Algebraic characterization, discrete Wigner distribution, linear redundancy, time–frequency analysis. I.
Dirty RF
, 2004
"... Future wireless communications systems are expected to provide ever higher data rates. Still, devices have to be produced at reasonable cost in order to be affordable to customers. The widely known impairments  "dirt effects"  in analog RF tend to aggravate as we go for the large trans ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
Future wireless communications systems are expected to provide ever higher data rates. Still, devices have to be produced at reasonable cost in order to be affordable to customers. The widely known impairments  "dirt effects"  in analog RF tend to aggravate as we go for the large transmission bandwidths and high carrier frequencies that usually come with an increased data throughput.
Distributions In The Discrete Cohen Classes
"... The Cohen class of timefrequency distributions for continuous signals has recently been to extended to discrete signals using both an axiomatic approach and an operator theory approach. In this paper, we investigate the formulation of several classical timefrequency distributions (Wigner, Rihaczek, ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
The Cohen class of timefrequency distributions for continuous signals has recently been to extended to discrete signals using both an axiomatic approach and an operator theory approach. In this paper, we investigate the formulation of several classical timefrequency distributions (Wigner, Rihaczek, MargenauHill, Page, Levin, BornJordan, spectrogram) in the discrete Cohen classes. The main result of this paper concludes that there does not exist a formulation of the Wigner distribution in all of the discrete Cohen classes. 1. INTRODUCTION There are four types of signals often used in signal processing, and to analyze these signals, there are four types of Fourier transforms. In Table 1 we list the four types of signals along with their properties and the appropriate Fourier transform. Since the Fourier transform is linear, the discrete Fourier transforms are samples of the continuous Fourier transform under the appropriate sampling conditions. The Cohen class of timefrequency distr...