TL;DR: This paper gives an exposition of linear prediction in the analysis of discrete signals as a linear combination of its past values and present and past values of a hypothetical input to a system whose output is the given signal.
Abstract: This paper gives an exposition of linear prediction in the analysis of discrete signals The signal is modeled as a linear combination of its past values and present and past values of a hypothetical input to a system whose output is the given signal In the frequency domain, this is equivalent to modeling the signal spectrum by a pole-zero spectrum The major part of the paper is devoted to all-pole models The model parameters are obtained by a least squares analysis in the time domain Two methods result, depending on whether the signal is assumed to be stationary or nonstationary The same results are then derived in the frequency domain The resulting spectral matching formulation allows for the modeling of selected portions of a spectrum, for arbitrary spectral shaping in the frequency domain, and for the modeling of continuous as well as discrete spectra This also leads to a discussion of the advantages and disadvantages of the least squares error criterion A spectral interpretation is given to the normalized minimum prediction error Applications of the normalized error are given, including the determination of an "optimal" number of poles The use of linear prediction in data compression is reviewed For purposes of transmission, particular attention is given to the quantization and encoding of the reflection (or partial correlation) coefficients Finally, a brief introduction to pole-zero modeling is given
TL;DR: In this paper, a method is presented for determining the complex permittivity and permeability of linear materials in the frequency domain by a single time-domain measurement; typically, the frequency band extends from VHF through X band.
Abstract: In this paper a method is presented for determining the complex permittivity and permeability of linear materials in the frequency domain by a single time-domain measurement; typically, the frequency band extends from VHF through X band. The technique described involves placing an unknown sample in a microwave TEM-mode fixture and exciting the sample with a subnanosecond baseband pulse. The fixture is used to facilitate the measurement of the forward- and back-scattered energy, s21(t) and s11(t), respectively. It is shown in this paper that the forward- and back-scattered time-domain "signatures" are uniquely related to the intrinsic properties of the materials, namely, e* and ?*. By appropriately interpreting s21(t) and s11(t), one is able to determine the real and imaginary parts of ? and ? as a function of frequency. Experimental results are presented describing several familiar materials.
TL;DR: This research presents a meta-analysis of time series regression and exploratory data analysis on the basis of ARIMA models for state-space models and spectral analysis and filtering in the frequency domain.
Abstract: Characteristics of time series.- Time series regression and exploratory data analysis.- ARIMA models.- Spectral analysis and filtering.- Additional time domain topics.- State-space models.- Statistical methods in the frequency domain.
TL;DR: Results are presented which demonstrate the superior sensitivity of swept source (SS) and Fourier domain (FD) optical coherence tomography (OCT) techniques over the conventional time domain (TD) approach.
Abstract: We present theoretical and experimental results which demonstrate the superior sensitivity of swept source (SS) and Fourier domain (FD) optical coherence tomography (OCT) techniques over the conventional time domain (TD) approach. We show that SS- and FD-OCT have equivalent expressions for system signal-to-noise ratio which result in a typical sensitivity advantage of 20-30dB over TD-OCT. Experimental verification is provided using two novel spectral discrimination (SD) OCT systems: a differential fiber-based 800nm FD-OCT system which employs deep-well photodiode arrays, and a differential 1300nm SS-OCT system based on a swept laser with an 87nm tuning range.
TL;DR: By comparison with one-step, FFT-based reconstruction, time reversal is shown to be sufficiently general that it can also be used for finite-sized planar measurement surfaces and the optimization of computational speed is demonstrated through parallel execution using a graphics processing unit.
Abstract: A new, freely available third party MATLAB toolbox for the simulation and reconstruction of photoacoustic wave fields is described. The toolbox, named k-Wave, is designed to make realistic photoacoustic modeling simple and fast. The forward simulations are based on a k-space pseudo-spectral time domain solution to coupled first-order acoustic equations for homogeneous or heterogeneous media in one, two, and three dimensions. The simulation functions can additionally be used as a flexible time reversal image reconstruction algorithm for an arbitrarily shaped measurement surface. A one-step image reconstruction algorithm for a planar detector geometry based on the fast Fourier transform (FFT) is also included. The architecture and use of the toolbox are described, and several novel modeling examples are given. First, the use of data interpolation is shown to considerably improve time reversal reconstructions when the measurement surface has only a sparse array of detector points. Second, by comparison with one-step, FFT-based reconstruction, time reversal is shown to be sufficiently general that it can also be used for finite-sized planar measurement surfaces. Last, the optimization of computational speed is demonstrated through parallel execution using a graphics processing unit.