This paper addresses the problem of designing signals for general group representations subject to constraints which are formulated as convex sets in the Hilbert space of the group states. In particular, the paper con...
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This paper addresses the problem of designing signals for general group representations subject to constraints which are formulated as convex sets in the Hilbert space of the group states. In particular, the paper considers irreducible representations in an infinite dimensional Hilbert space and derives an iterative procedure for proceeding from an arbitrary element of the Hilbert space to a state of the group subject to a priori imposed constraints with closed convex range. As examples, the paper focusses on narrowband and wideband radar ambiguity synthesis.
Focussing techniques have proven efficient in direction-of-arrival estimation of broadband signals. However, when used alone at high frequency operation, these techniques cannot accurately locate the sources, due to t...
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Focussing techniques have proven efficient in direction-of-arrival estimation of broadband signals. However, when used alone at high frequency operation, these techniques cannot accurately locate the sources, due to the numerous spurious peaks in the spectrum. Since the spurious peaks depend on the array manifold, their location varies from one focussing frequency to another. Improved jammer localization can, therefore, be achieved by focussing at different frequencies and then averaging the corresponding MUSIC spectra. The averaging smooths out the undesired peaks while boosting the common spectral peaks, allowing correct detection and location of the waveforms impinging on the array.
The scale dependent wavelet transform can be augmented by a rotation dependent version as well as other generalizations. Tomographic analysis and line segment transforms are special cases of rotation dependent wavelet...
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The scale dependent wavelet transform can be augmented by a rotation dependent version as well as other generalizations. Tomographic analysis and line segment transforms are special cases of rotation dependent wavelet analysis. Other cases suggested by biological analogy9 are a rotation dependent edge segment transform (using edge segments rather than line segments) and a binocular rotation dependent wavelet transform that introduces depth information into the reconstructed image. Applications to robot vision and synthetic aperture radar appear particularly promising.
We develop redundant CORDIC scheme where the scale factor is forced to be constant while computing angles for 2 × 1 plane rotations. Based on the scheme, we present a fixed-point implementation of matrix triangul...
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We develop redundant CORDIC scheme where the scale factor is forced to be constant while computing angles for 2 × 1 plane rotations. Based on the scheme, we present a fixed-point implementation of matrix triangularization by Luk's parallel algorithm, with the following additional features: (1) the final scaling operation is done by shifting, (2) the number of iterations in CORDIC rotation unit is reduced by about 25% by expressing the direction of the rotation in radix-2 and radix-4, and (3) the conventional number representation of rotated output is obtained on-the-fly, not from a carry-propagate adder. The number of hardware modules and the speed are evaluated and compared with the previous CORDIC schemes.
This paper presents a generalized parametric estimator for the directions of arrival (DOA) of wide-band signals. This estimator is derived by extenting the geometrical explanation of the ML estimator of narrow-band si...
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This paper presents a generalized parametric estimator for the directions of arrival (DOA) of wide-band signals. This estimator is derived by extenting the geometrical explanation of the ML estimator of narrow-band signals to the focussed correlation matrix. The consistency of the estimator for estimating DOA has been proved. This estimator can be considered as a coherent signalprocessing method by which the computation complexity can be reduced approximately by the number of the frequency bins. We have also shown that under certain condition the proposed estimator is equivalent to the ML estimator derived by applying the likelihood principle on the Fourier coefficients of each frequency bin. Such an equivalence implies that the MLE has some inherent advantages from the perspective of improving performance and that the focussing techniques are not necessary for the ML estimator.
This paper examines the problem of instantaneous frequency (IF) estimation for Frequency Modulated (FM) signals imbedded in white Gaussian noise. It reviews currently available techniques, and in addition, proposes so...
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This paper examines the problem of instantaneous frequency (IF) estimation for Frequency Modulated (FM) signals imbedded in white Gaussian noise. It reviews currently available techniques, and in addition, proposes some new ones, based on a modelling of the signal phase as a polynomial. Both linear least-squares techniques and Maximum Likelihood (ML) techniques are investigated for estimating the polynomial coefficients. It is seen that the linear least squares approach is efficient (i.e. unbiased and meets the Cramer-Rao bounds) for high SNR, while the ML scheme is efficient for a much larger range of SNR. Theoretical lower variance bounds are given for estimating the polynomial coefficients and are compared with the results of simulations. Guidelines are given as to which estimation method should be used for a given signal class and signal to Noise Ratio (SNR) level.
The Fourier-Mellin transform (FMT) of an input function is defined as and is the magnitude squared of the Mellin transform of the magnitude squared of the Fourier transform of the input function. As such, the FMT is u...
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The Fourier-Mellin transform (FMT) of an input function is defined as and is the magnitude squared of the Mellin transform of the magnitude squared of the Fourier transform of the input function. As such, the FMT is unchanged by translations and dilations of the input function. While the FMT has found applications in optical pattern recognition, ship classification by sonar and radar, and image processing, only cursory attention has been paid to the truncation error incurred by using a finite number of samples of the input function. This paper establishes truncation bounds for computing the FMT for band-limited functions from a finite number of samples of the input function. These bounds naturally suggest an implementation of the FMT by the method of direct expansions. This approach readily generalizes to a direct expansion for the Wigner-Ville distribution and the Q distribution.
Effective signal detection and feature extraction in noisy environments generally depend on exploiting some knowledge of the signal. When the signal is exactly known, the matched filter is the optimum signal processin...
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Effective signal detection and feature extraction in noisy environments generally depend on exploiting some knowledge of the signal. When the signal is exactly known, the matched filter is the optimum signalprocessing strategy. Other signalprocessing strategies succeed when the signal detail is but partially known. The short-time Fourier transform and the Gabor transform are two methods that exploit signal envelope information. The former is a well known and widely used representation which is important in many fields. The related but distinct Gabor transform has been less frequently used, but has features absent in Fourier analysis. This paper compares the two transforms and makes the case that the Gabor representation can often be the more compact, and may require substantially less computation and storage in some applications. There is a sense in which the Gabor achieves a preferential trade of signal-to-noise ratio for resolution, and because of this, one can also expect better signal recognition and feature reconstructions from the Gabor transform in the presence of noise.
This paper describes the application of the theory of projections onto convex sets to time-frequency filtering and synthesis problems. We show that the class of Wigner-Ville Distributions (WVD) of L2 signals form the ...
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This paper describes the application of the theory of projections onto convex sets to time-frequency filtering and synthesis problems. We show that the class of Wigner-Ville Distributions (WVD) of L2 signals form the boundary of a closed convex subset of L2(R2). This result is obtained by considering the convex set of states on the Heisenberg group, of which the ambiguity functions form the extreme points. The form of the projection onto the set of WVDs is deduced. Various linear and non-linear filtering operations are incorporated by formulation as convex projections. An example algorithm for simultaneous time-frequency filtering and synthesis is suggested.
We consider the problem of detecting a known Gaussian random transient in the presence of a strong, known, random, Gaussian, narrowband interference. This can be regarded as a special case of the classical problem of ...
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We consider the problem of detecting a known Gaussian random transient in the presence of a strong, known, random, Gaussian, narrowband interference. This can be regarded as a special case of the classical problem of detecting a known Gaussian random signal in known Gaussian colored noise. There exists a standard solution for such a problem, based on the classical optimum detector for random signals in noise. However, such a detector does not explicitly use the non-stationary character of the signal as a priori available information. Reformulation of the optimum detection in the time-frequency plane allows one to exploit this distinguishing signal feature and suppress the stationary interference and noise. This is accomplished here by use of the Wigner-Ville signal representation and an optimum signal/noise subspace decomposition that maximizes the transient signal to noise ratio. The new detection procedure eliminates the subspace where major part of the energy of random noise sample will fall while retaining almost all of the signal energy. In this fashion, a gain in the output signal to noise ratio is achieved as verified by simulations.
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