Journal ArticleDOI
Generalization of the Wiener-Khinchin theorem
TLDR
A full generalization is presented where both the autocorrelation function and power spectral density are defined in terms of a general basis set and a partial generalization where the density is the Fourier transform of the characteristic function but the characteristicfunction is defined in Terms of an arbitrary basis set.Abstract:
We generalize the concept of the autocorrelation function and give the generalization of the Wiener-Khinchin theorem. A full generalization is presented where both the autocorrelation function and power spectral density are defined in terms of a general basis set. In addition, we present a partial generalization where the density is the Fourier transform of the characteristic function but the characteristic function is defined in terms of an arbitrary basis set. Both the deterministic and random cases are considered.read more
Citations
More filters
Proceedings ArticleDOI
Road condition monitoring using on-board Three-axis Accelerometer and GPS Sensor
TL;DR: Experimental results show that RCM-TAGPS can evaluate pavement roughness level correctly, even under some interference like potholes, manholes and decelerating belts, and the total cost of RCM -TAGPS in each vehicle is no more than 50 dollars, which is about 1/4400 to 1/160 of the existing system used in civil engineering and municipal engineering.
Book ChapterDOI
From Stationarity to Self-similarity, and Back: Variations on the Lamperti Transformation
TL;DR: The Lamperti transformation as mentioned in this paper defines a one-to-one correspondence between stationary processes on the real line and self-similar processes in the real half-line, and has been applied in many applications.
Journal ArticleDOI
Single channel nonstationary stochastic signal separation using linear time-varying filters
James R. Hopgood,Pjw Rayner +1 more
TL;DR: The paper shows that when signals are separated using the generalized Wiener filter, the degree of separability can be deduced from the signal structure.
Journal ArticleDOI
Meteoric smoke particle properties derived using dual-beam Arecibo UHF observations of D-region spectra during different seasons
TL;DR: In this article, a seasonal study of the presence and characteristics of meteoric smoke particles (MSPs) in the D-region plasma derived from observations using the Gregorian and line feeds of the 430 MHz dual-beam Arecibo Observatory (AO) incoherent scatter radar (ISR) in Puerto Rico (18 ∘ N, 67 ∘ W ) is presented.
Journal ArticleDOI
Acoustic data condensation to enhance pipeline leak detection
TL;DR: Experimental results show that the proposed method can transform the original acoustic signals into a smaller number of featured predictors, even less than ten-thousandths of the original data amount, while improving classification accuracy despite loud machine-driven noises nearby.
References
More filters
Book
Time-Frequency Analysis
TL;DR: In this article, the authors present a general approach and the Kernel Method for reduced interference in the representation of signal signals, which is based on the Wigner distribution and the characteristic function operator.
Book
Probability, Random Variables and Random Signal Principles
TL;DR: 1 Probability 2 The Random Variable 3 Operations on one Random Variable--Expectation 4 Multiple Random Variables 5 Operations of Multiple Randomvariables 6 Random Processes-Temporal Characteristics 7 Random processes-Spectral Characteristics 8 Linear Systems with Random Inputs 9 Optimum Linear Systems 10 Some Practical Applications of the Theory.
Journal ArticleDOI
The scale representation
TL;DR: The authors considers "scale" a physical attribute of a signal and develop its properties which allows one to define the scale transform and the energy scale density spectrum which is an indication of the intensity of scale values in a signal.
Book
Group representations and applied probability
TL;DR: In this paper, the authors present an introduction to certain mathematical ideas which can be of considerable importance in applied probability and in statistical theory and assume some knowledge of the groups, though most concepts are defined below.
Journal ArticleDOI
A class of second-order stationary self-similar processes for 1/f phenomena
TL;DR: This study proposes a class of statistically self-similar processes and outlines an alternative mathematical framework for the modeling and analysis of 1/f phenomena based on the extensions of the basic concepts of classical time series analysis on the notion of stationarity.