## Mathematics in Signal ProcessingT. S. Durrani, J. B. Abbis, J. E. Hudson, R. N. Madan, J. G. McWhirter, T. A. Moore This book is based on the proceedings of the first I.M.A. International Conference on Mathematics in Signal Processing, the purpose of which was to bring together mathematicians and signal processing experts to explore the many areas of mutual interest and identify fruitful avenues for further research. The rich variety of papers presented here is clear evidence that this goal was achieved. The contributors' findings are divided into six categories: Signal Analysis and Modelling; Spectral Analysis; Inverse Problems; Image Reconstruction; Numerical Algorithms and Architectures; and Adaptive Techniques. A wealth of new ideas and interesting reading is presented for mathematicians, scientists, and engineers working in signal processing. |

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### Contents

A unified theory of model reduction via Gleason measures | 15 |

Some new difference schemes for the prediction of | 33 |

Generalised sampling expansions using Taylor coefficients | 59 |

Copyright | |

16 other sections not shown

### Common terms and phrases

adaptive filter algorithm analysis applied approximation array assumed asymptotic autocorrelation bandlimited bounds Chebyshev components computed consider constraint convergence convex sets convolution correlation corresponding covariance matrix decomposition deconvolution defined denotes density derived Digital dimensional distribution eigenvalues elements equation error estimate example factor finite formula Fourier transform frequency Gaussian given Hence Hilbert space IEEE IEEE Trans image restoration impulse response input integer interpolation inverse iteration Kalman Kalman filter keystream least-squares linear multiplications norm obtained operator optimal orthogonal output parameter performance pixel point spread function polynomials prior problem Proc processor properties pulse radar reconstruction recursion reflection coefficients regularisation Riccati Equation samples self-tuning sensors sequence shown signal processing singular value singular value decomposition sinusoids solution solving spectral spectrum statistical sum-box filters target technique Theorem theory Toeplitz Toeplitz matrix update variance vector weight zero