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In this paper, the distributions of the largest and smallest eigenvalues of complex Wishart matrices and the condition number of complex Gaussian random matrices are derived. These distributions are represented by complex hypergeometric functions of matrix arguments, which can be expressed in terms of complex zonal polynomials. Several results are derived(More)
In this paper, we generalize the classical windowed Fourier transform (WFT) to quaternion-valued signals, called the quaternionic windowed Fourier transform (QWFT). Using the spectral representation of the quaternionic Fourier transform (QFT), we derive several important properties such as reconstruction formula, reproducing kernel, isometry, and(More)
In this paper we introduce the continuous quaternion wavelet transform (CQWT). We express the admissibility condition in terms of the (right-sided) quaternion Fourier transform. We show that its fundamental properties, such as inner product, norm relation, and inversion formula, can be established whenever the quaternion wavelets satisfy a particular(More)
A one-step 4-stage Hermite-Birkhoff-Taylor method of order 12, denoted by HBT(12)4, is constructed for solving nonstiff systems of first-order differential equations of the form y = f (x, y), y(x 0) = y 0. The method uses derivatives y to y (9) as in Taylor methods combined with a 4-stage Runge-Kutta method. Forcing an expansion of the numerical solution to(More)
Digital image compression with multiresolution singular value decomposition is compared with discrete cosine transform, discrete 9/7 biorthogonal wavelet transform, Karhunen –Lò eve transform, and combinations thereof. The coding methods used SPIHT and run-length with Huffmann coding. The performances of these methods differ little from each other.(More)
Quadratic forms on complex random matrices and their joint eigenvalue densities are derived with the goal of studying the ergodic channel capacity of multiple-input, multiple-output (MIMO) Rayleigh distributed wireless communication channels. We consider MIMO channels which are correlated at the transmitter and/or the receiver ends and evaluate the(More)
Variable-step variable-order 3-stage Hermite–Birkhoff–Obrechkoff methods of order 4 to 14, denoted by HBO(4-14)3, are constructed for solving non-stiff systems of first-order differential equations of the form y = f (x, y), y(x 0) = y 0. These methods use y and y as in Obrechkoff methods. Forcing a Taylor expansion of the numerical solution to agree with an(More)