A New Discrete Analytic Signal for Reducing Aliasing in the Discrete Wigner-Ville Distribution

It is not possible to generate an alias-free discrete Wigner--Ville distribution (DWVD) from a discrete analytic signal. This is because the discrete analytic signal must satisfy two mutually exclusive constraints. We present, in this article, a new discrete analytic signal that improves on the commonly used discrete analytic signal's approximation of these two constraints. Our analysis shows that---relative to the commonly used signal---the proposed signal reduces aliasing in the DWVD by approximately 50%. Furthermore, the proposed signal has a simple implementation and satisfies two important properties, namely, that its real component is equal to the original real signal and that its real and imaginary components are orthogonal

Accurate and efficient implementation of the time-frequency matched filter

The discrete time--frequency matched filter should replicate the continuous time--frequency matched filter. But the methods differ. To avoid aliasing the discrete method transforms the real-valued signal to the complex-valued analytic signal. The theory for the time--frequency matched filter does not consider the discrete case using the analytic signal. We find that the performance of the matched filter degrades when using the analytic, rather than real-valued, signal. This performance degradation is dependent on the signal to noise ratio and the signal type. In addition, we present a simple algorithm to efficiently compute the time--frequency matched filter. The algorithm with the real-valued signal, comparative to using the analytic signal, requires one-quarter of the computational load. Hence the real-valued signal---and not the analytic signal---enables an accurate and efficient implementation of the time--frequency matched filter

Pseudo Wigner-Ville Distribution, Computer program and its Applications to Time-Frequency Domain Problems

Machinery operating in non-stationary mode generates a signature which at each instant of time has a distinct frequency. A time-frequency domain representation is needed to characterize such signature. Pseudo Wigner-Ville distribution is ideally suited for portraying non-stationary signal in the time- frequency domain and carried out by adapting the fast Fourier transform algorithm. The important parameters affecting the pseudo Wigner-Ville distribution are discussed and sensitivity analyses are also performed. Practical examples of an actual transient signal are used to illustrate its dynamic features jointly in time and frequency.Naval Sea Systems Commandhttp://archive.org/details/pseudowignervill00jeonNaval Sea Systems CommandApproved for public release; distribution is unlimited

A Quantitative Measure of Mono-Componentness for Time-Frequency Analysis

Joint time-frequency (TF) analysis is an ideal method for analyzing non-stationary signals, but is challenging to use leading to it often being neglected. The exceptions being the short-time Fourier transform (STFT) and spectrogram. Even then, the inability to have simultaneously high time and frequency resolution is a frustrating issue with the STFT and spectrogram. However, there is a family of joint TF analysis techniques that do have simultaneously high time and frequency resolution – the quadratic TF distribution (QTFD) family. Unfortunately, QTFDs are often more troublesome than beneficial. The issue is interference/cross-terms that causes these methods to become so difficult to use. They require that the “proper” joint distribution be selected based on information that is typically unavailable for real-world signals. However, QTFDs do not produce cross-terms when applied to a mono-component signal. Clearly, determining the mono-componentness of a signal provides a key piece of information. However, until now, the means for determining if a signal is a monocomponent or a multi-component has been to choose a QTFD, generate the TF representation (TFR), and visually examine it. The work presented here provides a method for quantitatively determining if a signal is a mono-component. This new capability provides an important step towards finally allowing QTFDs to be used on multi-component signals, while producing few to no interference terms through enabling the use of the quadratic superposition property. The focus of this work is on establishing the legitimacy for “measuring” mono-componentness along with its algorithmic implementation. Several applications are presented, such as quantifying the quality of the decomposition results produced by the blind decomposition algorithm, Empirical Mode Decomposition (EMD). The mono-componentness measure not only provides an objective means to validate the outcome of a decomposition algorithm, it also provides a practical, quantitative metric for their comparison. More importantly, this quantitative measurement encapsulates mono-componentness in a form which can actually be incorporated in the design of decomposition algorithms as a viable condition/constraint so that true mono-components could be extracted. Incorporating the mono-component measure into a decomposition algorithm will eventually allow interference free TFRs to be calculated from multi-component signals without requiring prior knowledge

Analysis of lung auscultatory phenomena using the Wigner-Ville Distribution

In this paper the authors will try to discuss the applicability of Wigner-Ville Distribution for the digital analysis of auscultatory sounds. First of all, thte issues related to computer aided diagnosis are presented. Next, the methodology of research is shown and subsequently, the types of sounds are described. Another element of this work is the presentation of issues related to the digital signal processing including the Short-Time Fourier Transform(STFT), Wigner-Ville Distribution (WVD), and its variation- Smoothed Wigner-Ville Distribution (SWVD). This paper summarizes the results obtained using STFT and SWVD, showing SWVD more useful to detect the type of auscultatory sounds

Proofs for Discrete Time-Frequency Distribution Properties

This technical report contains proofs for a set of mathematical properties of a recently proposed discrete time-frequency distribution class

A Wigner Distribution Analysis of One Dimensional Scattering

We applied the Wigner Distribution Function, a distribution function of time and frequency based on an initial function of either of those variables, to a series of time based correlation functions. These time based correlation functions were the result of a 1-dimensional free particle wave packet, the reactant wave function, which had propagated through a quantum potential well and then had components of the reactant wave function that exited the opposite side of the well auto-correlated in time with a stationary 1-dimensional free particle wave packet, the product wave function. This process was undertaking in order to generate a 3-dimensional depiction, in time and frequency, of the reactant wave functions interaction with the quantum potential well. Fortran 77 code was utilized to generated the time propagation of the reactant wave function by means of the Split Operator Method, which was given the following initial set of conditions; x0 = -20 (Bohr radii), k0 = 3 (atomic units), and δ = 1 (Bohr radius). A series of potential wells with variable depths were implemented into the code. The code then computed the correlation in time of the exiting reactant wave function with a stationary wave function before applying the Wigner Distribution Function. When Wigner Distribution Function was applied to the time correlation function many recognizable features on the potential well were observed from the 3-dimensional plot generated including transmission resonance energy levels. The classical time of arrival was also captured by the Wigner Distribution Function. As a useful tool the Wigner Distribution Function provides more insight into the quantum interactions of chemical reactions in terms of time and frequency than traditional spectrographic analysis