## Signal Processing: A Mathematical ApproachA practical guide to the mathematics behind signal processing, this book provides the essential mathematical background and tools necessary to understand and employ signal processing techniques. Topics addressed include: - Fourier series and transforms in one and several variables, - applications to acoustic and electromagnetic propagation models, - transmission and emission tomography and image reconstruction, - optimization techniques, - high-resolution methods, and more. The emphasis is on the general problem of extracting information from limited data obtained by some form of remote sensing: acoustic or radar processing, satellite imaging, or medical tomographic scanning. |

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### Contents

Complex Exponentials | 5 |

Inner Products | 23 |

Discrete Linear Filters | 32 |

Copyright | |

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### Common terms and phrases

algorithm approximation assume autocorrelation band-limited extrapolation block-iterative calculate called Cauchy's inequality chapter coefficients column vector complex exponential complex numbers consider converges convex convex sets convolution covariance matrix data consistent defined delta functions denotes discrete discussion dot product eigenvalues eigenvectors EMML algorithm entries entropy estimate example Exercise exponential function finite Fourier series frequency function f(x Haar wavelet Hilbert transform inequality infinite sequence inner product integral interval inverse Fourier transform IPDFT iterative step Kullback-Leibler distance least-squares solution limit cycle linear equations linear system matrix Q maximization maximum method minimize noise nonnegative nonzero obtain optimal orthogonal parameter PDFT pixel planewave Poisson polynomial power spectrum prior problem random process random variables samples Show signal processing sinusoids solution of Ax solving Suppose system of equations system of linear theorem tomography vector f wavelet Wiener filter zero