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Topic: Radar ambiguity function

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Chirplet transform

Fourier transform

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	Another Symmetry
		There remains, however, the ambiguity introduced by squaring both sides of equation (2), suppressing the signs of the factors.
		Equation (2) itself, without squaring, is invariant under inversion of any two of the speeds, but the inversion of all three speeds changes the sign of the right side.
		Since there is only one odd elementary symmetric function of one variable, and likewise for two variables, the case of three variables is the first for which there exists a non-tautological expression of this form.
	www.mathpages.com /rr/s1-08/1-08.htm (2017 words)

	Autochirplet and Cross Chirplet Transforms (Site not responding. Last check: 2007-10-30)
		The `autochirplet ambiguity function' is not new, but, rather, was proposed by Berthonberthon as a generalization of the radar ambiguity function.
		Note that the radar ambiguity functionwoodward1,skolnik is a special case of (15).
		It is well known that the power spectrum is the Fourier transform of the autocorrelation function, and that the Wigner distribution is the two-dimensional (rotated) Fourier transform of the radar ambiguity function.
	wearcam.org /chirplet/node17.html (254 words)

	Range-Lag Ambiguity Function toolbox
		All functions accept a lag argument, specifying for which lags (in units of bauds) range-lag ambiguity functions are computed.
		The functions do not assume "correctness" or "completeness" of codes or code sets, and will happily accept incomplete or random alternating code sets (indeed this was part of the motivation for writing the functions in the first place), and it will also accept codes that aren't Barker codes as the Barker code argument.
		For alternating codes, the two-dimensional ambiguity functions for any given scan in the code set is ambiguous in range, only when the code set is decoded are these ambiguities reduced or, (for complete sets of Lehtinen-type alternating codes), eliminated.
	www.phys.uit.no /~tom/wtt (1423 words)

	EyeTap Personal Imaging Lab
		Siebert also considered chirping functions for pulse compression radar, and studied these in detail, observing that chirping in the time domain gives rise to a shearing in the time-frequency plane (or equivalently, a shearing in the 2D Fourier transform of the time-frequency plane).
		In 1989 and early 1990, we formulated the chirplet transform, a multidimensional parameter space whose coordinate axes correspond to the pure parameters of planar affine coordinate transformations in the time-frequency plane.
		Furthermore, we suggested using the work of Landaudps1[21][22][23][24][25] who introduced prolate spheroidal functions, and we noted their significance in the context of the shearing phenomenon in the time-frequency plane, as they form idealized parallelogram tilings of this plane.
	www.eyetap.org /wearcomp/chirplet/node2.html (751 words)

	Conjugate variables - Wikipedia, the free encyclopedia
		Position and momentum: precise measurements of position lead to ambiguity of momentum, and v.v.
		Doppler and range: the more we know about how far away a radar target is, the less we can know about the exact velocity of approach or retreat, and vice versa.
		In this case, the two dimensional function of doppler and range is known as a radar ambiguity function or radar ambiguity diagram.
	en.wikipedia.org /wiki/Canonical_conjugate_variables (233 words)

	Background
		It has been shown that the ambiguity function, while being an important representation in radar signal processing [3][2], is also a polar display of the optical transfer function (OTF) [4].
		As a graphical example of the utility of the ambiguity function as a measure of the OTF, consider figures 1 and 2.
		Figure 1 is the ambiguity function related to a rectangular aperture with a normalized half-length of unity.
	www.colorado.edu /isl/papers/aberration/node2.html (556 words)

	Launchspace - Course Catalog
		The course begins with fundamentals (frequency, wavelength); moves rapidly to introduce the radar range equation; and then provides summaries of radar hardware, antennas, radar cross section, clutter, external noise, detection processing, the ambiguity function, monopulse, and the accuracy of radar measurements.
		Radar hardware: typical block diagram; transmitters; receivers/exciters; analog-to-digital converters; in-phase and quadrature (I and Q); noise figure; phase noise; waveguides.
		He then contributed to the development of a series of imaging instrumentation radars, which are operated on outdoor and indoor radar ranges.
	launchspace.santasoft.com /3000.htm (891 words)

	Radar Systems Analysis and Design Using MATLAB 2nd Ed
		Ideal for graduate study in radar system fundamentals and design or for professional reference, and featuring an abundance of MATLAB programs and code, Radar Systems Analysis and Design Using MATLAB, Second Edition presents the fundamentals and principles of radar along with enough rigorous mathematical derivations to ensure that readers gain a deep understanding.
		The author has extensively revised chapters on radar cross-section and polarization, matched filter and radar ambiguity function, and radar wave propagation.
		With all MATLAB functions updated to reflect version 7.0 and an expanded set of end-of-chapter problems, readers will find this up-to-date text to be the most complete treatment of radar available, providing the hands-on tools that will enrich their learning.
	www.scitechpub.com /Mahafza_Radar_Systems2nd.htm (333 words)

	[No title]
		Function $f:\Space{R}{n}\rightarrow\Cliff{0}{n}$ is called {\em monogenic\/} if it satisfies the {\em Dirac equation\/} \begin{equation}\label{eq:dirac} Df:=\frac{\partial f(y)}{\partial y_0} -\sum_{j=1}^n X_j\frac{\partial f(y)}{\partial y_j}=0\ \mbox{ or }\ \frac{\partial f(y)}{\partial y_0} =\sum_{j=1}^n X_j\frac{\partial f(y)}{\partial y_j}.
		Thus we may consider the function $\breve{f}(y_0,y_1,\ldots y_n)$ of $n+1$ variables as {\em analytical expansion\/} for the function $f(y_1,\ldots,y_n)$ of $n$ variables (compare with~\cite{Laville91}).
		Indeed, we have defined a relative convolution as a function of operators $X_j$ representing a Lie algebra \algebra{g}.
	www.ma.utexas.edu /mp_arc/papers/94-305 (9590 words)

	Historical Notes
		Beginning around 1956, Siebert began to formulate a radar detection philosophy with some particularly useful insights in terms of time-frequencysiebertphilosophy[9].
		Much of his insight was obtained through the use of Woodward's uncertainty functionsiebert, also known as the radar ambiguity functionskolnik or the Fourier-Wigner transformfolland.
		Later, we applied the chirplet transform and some of the new two-dimensional subspace transforms to problems in marine radar and obtained results that were better than previous methods, so we published these findingsmannVI91.
	wearcam.org /chirplet/node2.html (750 words)

	AMS Glossary
		—In radar, a two-dimensional function of radar range and Doppler frequency, determined by the transmitted waveform, that defines the effective filter response of the radar receiver.
		The ambiguity function is used to examine the suitability of different transmitted waveforms for achieving accuracy, resolution, freedom from ambiguities, and reduction of unwanted clutter.
		In particular, it defines 1) the sidelobe response to a complex radar waveform at different Doppler frequencies, and 2) the response of a receiver to targets at other ranges and Doppler frequencies from the desired target.
	amsglossary.allenpress.com /glossary/browse?s=a&p=47 (596 words)

	Abstracts
		After presenting the technical basis for such a radar, we describe an instrument that we are building at the University of Washington to study high-latitude plasma irregularities in the E region.
		Further understanding of auroral electrojet irregularities is impeded by precision limitations of existing instruments, by radar data which may seem incompatible, by the usually poor knowledge of the ambient conditions during these experiments, and by some confusion in the nomenclature (e.g.
		The ambiguity function of FM radio signals is measured using simulations and from this further simulations are performed to model the three methods of detecting targets.
	rrsl.ee.washington.edu /abstracts.html (3187 words)

	Wiley::Radar Signals
		Radar Signals is a comprehensive tutorial and overview of waveforms used in radar systems.
		The book dwells on the important role of the matched filter in radar signal processing and makes extensive use of the ambiguity function to describe the resolution and response, in range and Doppler.
		Practical aspects of radar signal processing are also considered, such as weighting, mismatch, Doppler filtering, and stretch processing.
	www.wiley.com /WileyCDA/WileyTitle/productCd-0471663077,subjectCd-EE29,descCd-description.html?print=true (132 words)

	EE 254 - Principles of Radar Systems
		A personal and technical account of the development of airborne radar in Britain and America during World War II, and of the scientific outgrowth is this work in subsequent years.
		Useful material on interpreting radar echoes from rough surfaces is included as well as radar results for the inner solar system.
		Rare exposition of development of radar and sonar in Germany during WWII and subsequently.
	www.stanford.edu /class/ee254/references.shtml (1108 words)

	IEEE 2002 Radar Conference April 22-25 in Long Beach, CA
		The principles, motivations, and terminology related to radar pulse compression are presented with an emphasis on obtaining a fundamental understanding of the concepts and techniques involved.
		The course closes with a discussion of innovative mismatch filtering techniques and the analysis and evaluation of pulse compression schemes based on application of the radar ambiguity function.
		He also is CEO of his firm, IRTA/MCA, which supplies expert consulting services to government, industry, and academia, in the areas of target identification, identification fusion, pulse compression, advanced radar concepts and developments, and the conduct of large, complex technical programs.
	www.ewh.ieee.org /r6/lac/radar02/tutorials/4.3.html (344 words)

	updated ee254 syllabus (Site not responding. Last check: 2007-10-30)
		This is an introductory course intended to provide you with the fundamentals as a basis for reading the literature, further study, and the use of radars and radar observations in research.
		After completion of this course you should be able to accomplish and analyze simple radar designs at the systems level, and to understand the operation of complex radars, at least qualitatively.
		'Radar' is an exciting subject which incorporates concepts and results from a range of electrical engineering and other disciplines to synthesize new systems and techniques for remote sensing and measurements.
	www-ee.stanford.edu /~zebker/ee254win2002/syllabus.ee254.html (888 words)

	Computer books at discount prices - nerdbooks.com
		As radar technology evolves to encompass a growing spectrum of applications in military, aerospace, automotive, and other sectors, innovations in digital signal processing have risen to meet the demand.
		Radar Signals features in-depth coverage of the most prevalent classical and modern radar signals used today, as well as new signal concepts developed in recent years.
		Combining lucid explanation, preferred signal tables, MATLAB codes, and problem sets in each chapter, Radar Signals is an essential reference for professionals-and a systematic tutorial for any seeking to broaden their knowledge base in this dynamic field.
	www.nerdbooks.com /item.php?id=0471473782 (183 words)

	The Wavelet Digest :: View topic - Preprints: Physical wavelets and radar
		ambiguity functions is generalized to the context of "physical
		functional reduces to the usual wideband ambiguity function, which is
		reduces to the narrowband ambiguity function, which is just the
	www.wavelet.org /phpBB2/viewtopic.php?t=3102&view=next (252 words)

	[No title]
		A typical example of energy functional we consider is the one given by the nonparametric area integrand $f(x, \xi) = \sqrt{1 + \Vert \xi \Vert^2}$, which corresponds with the time-dependent minimal surface equation.
		The new ingredient is the use of holomorphic functions with precise growth restrictions in the construction of explicit solutions to the equation.
		The process of translation averaging is known to improve dyadic BMO to the space BMO of functions of bounded mean oscillation, in the sense that the translation average of a family of dyadic BMO functions is necessarily a BMO function.
	projecteuclid.org /Dienst?verb=ListRecords&metadataPrefix=oai_dc&set=rmi (6555 words)

	Modeling of FM broadcast signals for use in bistatic radar applications
		The purpose of this project is threefold: To determine the optimum range-Doppler characteristics of an FM broadcast, to characterize a typical FM broadcast signal in terms of the properties of the ambiguity function, and to develop a model for the FM broadcast signal as a band-limited multi-tone FM stochastic process.
		The analysis of these signals is performed in the range-Doppler domain by observing the behavior of the ambiguity function.
		In contrast, the ambiguity function of a typical broadcast will exhibit a wider mainlobe and higher sidelobes.
	digitalcommons.utep.edu /dissertations/AAI1423722 (255 words)

	Citebase - Hermite functions and uncertainty principles for the Fourier and the windowed Fourier transforms (Site not responding. Last check: 2007-10-30)
		Hermite functions and uncertainty principles for the Fourier and the windowed Fourier transforms
		We then obtain similar results for the windowed Fourier transform (also known, up to elementary changes of functions, as the radar ambiguity function or the Wigner transform).
		Citation coverage and analysis is incomplete and hit coverage and analysis is both incomplete and noisy.
	citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:math/0102111 (565 words)

	[No title] (Site not responding. Last check: 2007-10-30)
		The processor ambiguity function and the radar distortion matrices are then combined to form a generalized polarimetric ambiguity function.
		The polarimetric ambiguity function of the SAR is then found using a single point target, namely a trihedral corner reflector.
		Based on the resultant polarimetric ambiguity function, an estimate for the backscattering coefficient of the terrain is found using a modified version of the STCT technique [5].
	www.eecs.umich.edu /RADLAB/sar_image_lab/umCalSAR.html (206 words)

	Math 8600 Syllabus
		Let f(t) be a real or complex-valued function on the real line R (or on the integers) and square integrable.
		Almost all of these methods are based on the decomposition of the Hilbert space of square integrable functions into orthogonal subspaces.
		Group representation theory lies at the core of the applied topics, particularly in its relationship to multi-scale analysis and self-similarity, and I will develop a bit of group theory as needed.
	www.ima.umn.edu /~miller/harmonic_analysis_intro.html (306 words)

	Time-Frequency Transforms for Radar Imaging and Signal Analysis
		It teaches you more efficient ways to extract dispersive scattering features; detect and extract weak signals in noise; form clear radar images; estimate parameters and perform motion compensation; detect and track moving targets in the synthetic aperture radar; and analyze vibration and rotation induced micro-Doppler.
		Moreover, the authors discuss future trends in time-frequency to analyze micro-Doppler, and provide you with a newly developed time-frequency approach to radar signal and image processing to help you solve problems associated with conventional approaches.
		Radar Signals, Radar Ambiguity Function and Matched Filter.
	www.scitechpub.com /Chen.htm (375 words)

	Description d'article (Site not responding. Last check: 2007-10-30)
		In this paper, we pursue the study of the radar ambiguity problem started in [Ja,GJP].
		More precisely, for a given function u we ask for all functions v (called ambiguity partners) such that the ambiguity functions of u and have same modulus.
		In some cases, v may be given by some elementary transformation of u and is then called a trivial partner of u otherwise we call it a strange partner.
	www.univ-orleans.fr /mapmo/membres/jaming/article.php?id=0&hide=true (206 words)

	On the Use of High Order Ambiguity Function for Multicomponent Polynomial Phase Signals - Wang, Zhou (ResearchIndex) (Site not responding. Last check: 2007-10-30)
		High-order ambiguity function (HAF) was first introduced to estimate the parameters of a single component PPS, but has not been widely used for multi-component PPS because of its nonlinearity.
		Multi-component PPS arise for example, in Doppler radar applications when multiple objects are tracked simultaneously.
		Wang and G. Zhou, "On the use of high-order ambiguity function for multi-component polynomial phase signals", Signal Processing, vol.
	citeseer.ist.psu.edu /306284.html (601 words)

	Boston University - ECE Department
		Functions, graphs, mathematical structures, morphisms, algebraic structures, semigroups, quotient groups, finite-state machines, their homomorphism, and simulation.
		Advanced topics include modeling (state space, transfer function matrix), MIMO poles and zeroes, controllability and observability, stability and robustness, structured and unstructured perturbations, the small gain theorem, optimization theory, and the Maximum Principle.
		Covers classification with likelihood functions and general discriminant function, density estimation, supervised and unsupervised learning, decision trees, feature reduction, performance estimation, and classification using sequential and contextual information, including Markov and hidden Markov models.
	www.bu.edu /dbin/ece/web/grad/courses.html (4891 words)

	Category Browsing Results
		Prediction, reduction, and measurement of electromagnetic scattering from complex three dimensional targets is the primary emphasis of this text, developed by the author from courses taught at the Naval Postgraduate School.
		It defines common terms and principles used in the field of radar and electronic warfare and describes the response of radar systems terms to electronic warfare and describes he response of radar systems to electronic countermeasures.
		During the last decade of the 20th century, radar technology has advanced at a breathtaking pace.
	opamp.com /cf/browse.cfm?Main=ELECTRONICS/COMMUNICATIONS&Sub1=RADAR (950 words)

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