Window Functions and Their Applications in Signal Processing

Window functions—otherwise known as weighting functions, tapering functions, or apodization functions—are mathematical functions that are zero-valued outside the chosen interval. They are well established as a vital part of digital signal processing. Window Functions and their Applications in Signal Processing presents an exhaustive and detailed account of window functions and their applications in signal processing, focusing on the areas of digital spectral analysis, design of FIR filters, pulse compression radar, and speech signal processing. Comprehensively reviewing previous research and recent developments, this book: Provides suggestions on how to choose a window function for particular applications Discusses Fourier analysis techniques and pitfalls in the computation of the DFT Introduces window functions in the continuous-time and discrete-time domains Considers two implementation strategies of window functions in the time- and frequency domain Explores well-known applications of window functions in the fields of radar, sonar, biomedical signal analysis, audio processing, and synthetic aperture rada

Window Functions and Their Applications in Signal Processing

Window functions—otherwise known as weighting functions, tapering functions, or apodization functions—are mathematical functions that are zero-valued outside the chosen interval. They are well established as a vital part of digital signal processing. Window Functions and their Applications in Signal Processing presents an exhaustive and detailed account of window functions and their applications in signal processing, focusing on the areas of digital spectral analysis, design of FIR filters, pulse compression radar, and speech signal processing. Comprehensively reviewing previous research and recent developments, this book: Provides suggestions on how to choose a window function for particular applications Discusses Fourier analysis techniques and pitfalls in the computation of the DFT Introduces window functions in the continuous-time and discrete-time domains Considers two implementation strategies of window functions in the time- and frequency domain Explores well-known applications of window functions in the fields of radar, sonar, biomedical signal analysis, audio processing, and synthetic aperture rada

Mutual Information Based Pilot Design for ISAC

The following paper presents a novel orthogonal pilot design dedicated for dual-functional radar and communication (DFRC) systems performing multi-user communications and target detection. After careful characterization of both sensing and communication metrics based on mutual information (MI), we propose a multi-objective optimization problem (MOOP) tailored for pilot design, dedicated for simultaneously maximizing both sensing and communication MIs. Moreover, the MOOP is further simplified to a single-objective optimization problem, which characterizes trade-offs between sensing and communication performances. Due to the non-convex nature of the optimization problem, we propose to solve it via the projected gradient descent method on the Stiefel manifold. Closed-form gradient expressions are derived, which enable execution of the projected gradient descent algorithm. Furthermore, we prove convergence to a fixed orthogonal pilot matrix. Finally, we demonstrate the capabilities and superiority of the proposed pilot design, and corroborate relevant trade-offs between sensing MI and communication MI. In particular, significant signal-to-noise ratio (SNR) gains for communication are reported, while re-using the same pilots for target detection with significant gains in terms of probability of detection for fixed false-alarm probability. Other interesting findings are reported through simulations, such as an \textit{information overlap} phenomenon, whereby the fruitful ISAC integration can be fully exploited

Methods in wave propagation and scattering

Supervised by Jin A. Kong.Also issued as Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2001.Includes bibliographical references (p. 195-213).by Henning Braunisch

Methods in wave propagation and scattering

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2001.Vita.Includes bibliographical references (p. 195-213).This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Aspects of wave propagation and scattering with an emphasis on specific applications in engineering and physics are examined. Frequency-domain methods prevail. Both forward and inverse problems are considered. Typical applications of the method of moments to rough surface three-dimensional (3-D) electromagnetic scattering require a truncation of the surface considered and call for a tapered incident wave. It is shown how such wave can be constructed as a superposition of plane waves, avoiding problems near both normal and grazing incidence and providing clean footprints and clear polarization at all angles of incidence. The proposed special choice of polarization vectors removes an irregularity at the origin of the wavenumber space and leads to a wave that is optimal in a least squared error sense. Issues in the application to 3-D scattering from an object over a rough surface are discussed. Approximate 3-D scalar and vector tapered waves are derived which can be evaluated without resorting to any numerical integrations. Important limitations to the accuracy and applicability of these approximations are pointed out. An analytical solution is presented for the electromagnetic induction problem of magnetic diffusion into and scattering from a permeable, highly but not perfectly conducting prolate spheroid under axial excitation, expressed in terms of an infinite matrix equation. The spheroid is assumed to be embedded in a homogeneous non-conducting medium as appropriate for low-frequency, high-contrast scattering governed by magnetoquasistatics. The solution is based on separation of variables and matching boundary conditions where the prolate spheroidal wavefunctions with complex wavenumber parameter are expanded in terms of spherical harmonics. For small skin depths, an approximate solution is constructed, which avoids any reference to the spheroidal wavefunctions. The problem of long spheroids and long circular cylinders is solved by using an infinite cylinder approximation. In some cases, our ability to evaluate the spheroidal wavefunctions breaks down at intermediate frequencies. To deal with this, a general broadband rational function approximation technique is developed and demonstrated. We treat special cases and provide numerical reference data for the induced magnetic dipole moment or, equivalently, the magnetic polarizability factor. The magnetoquasistatic response of a distribution of an arbitrary number of interacting small conducting and permeable objects is also investigated. Useful formulations are provided for expressing the magnetic dipole moment of conducting and permeable objects of general shape. An alternative to Tikhonov regularization for deblurring and inverse diffraction, based on a local extrapolation scheme, is described, analyzed, and illustrated numerically for the cases of continuation of fields obeying Laplace and Helmholtz equations. At the outset of the development, a special deconvolution problem, where a parameter describes the degree of additive blurring, is considered. No a priori knowledge on the unblurred data is assumed. A standard solution based on an output least squares formulation includes a regularization parameter into a linear, shift-invariant filter. The proposed alternative approach takes advantage of the analyticity of the smoothing process with respect to the blurring parameter. Here a simple local extrapolation scheme is employed. The problem is encountered in applications involving potential theories dealing with magnetostatics, electrostatics, and gravity data. As a generalization to the dynamic case, inverse diffraction of scalar waves is considered. Examples are presented and the two methods compared numerically. The problem of inferring unknown geometry and material parameters of a waveguide model from noisy samples of the associated modal dispersion curves is considered. In a significant reduction of the complexity of a common inversion methodology, the inner of two nested iterations is eliminated: The approach described does not employ explicit fitting of the data to computed dispersion curves. Instead, the unknown parameters are adjusted to minimize a cost function derived directly from the determinant of the boundary condition system matrix. This results in a very efficient inversion scheme that, in the case of noise-free data, yields exact results. Multi-mode data can be simultaneously processed without extra complications. Furthermore, the inversion scheme can accommodate an arbitrary number of unknown parameters, provided that the data have sufficient sensitivity to these parameters. As an important application, the sonic guidance condition for a fluid-filled borehole in an elastic, homogeneous, and isotropic rock formation is considered for numerical forward and inverse dispersion analysis. The parametric inversion with uncertain model parameters and the influence of bandwidth and noise are investigated numerically. The cases of multi-frequency and multi-mode data are examined. Finally, the borehole leaky-wave modes are classified according to the location of the roots of the characteristic equation on a multi-sheeted Riemann surface. A comprehensive set of dipole leaky-wave modal dispersions is computed. In an independent numerical experiment the excitation of some of these modes is demonstrated. The utilization of leaky-wave dispersion data for inversion is discussed.by Henning Braunisch.Ph.D

Investigating the build-up of precedence effect using reflection masking

The auditory processing level involved in the build‐up of precedence [Freyman et al., J. Acoust. Soc. Am. 90, 874–884 (1991)] has been investigated here by employing reflection masked threshold (RMT) techniques. Given that RMT techniques are generally assumed to address lower levels of the auditory signal processing, such an approach represents a bottom‐up approach to the buildup of precedence. Three conditioner configurations measuring a possible buildup of reflection suppression were compared to the baseline RMT for four reflection delays ranging from 2.5–15 ms. No buildup of reflection suppression was observed for any of the conditioner configurations. Buildup of template (decrease in RMT for two of the conditioners), on the other hand, was found to be delay dependent. For five of six listeners, with reflection delay=2.5 and 15 ms, RMT decreased relative to the baseline. For 5‐ and 10‐ms delay, no change in threshold was observed. It is concluded that the low‐level auditory processing involved in RMT is not sufficient to realize a buildup of reflection suppression. This confirms suggestions that higher level processing is involved in PE buildup. The observed enhancement of reflection detection (RMT) may contribute to active suppression at higher processing levels