Mathematical Methods and Algorithms for Signal Processing by Todd K. Moon

By Todd K. Moon

Mathematical equipment and Algorithms for sign Processing tackles the problem of delivering readers and practitioners with the wide instruments of arithmetic hired in sleek sign processing. construction from an assumed history in indications and stochastic methods, the booklet offers an exceptional beginning in research, linear algebra, optimization, and statistical sign processing. attention-grabbing glossy subject matters now not to be had in lots of different sign processing books; similar to the EM set of rules, blind resource operation, projection on convex units, etc., as well as many extra traditional subject matters equivalent to spectrum estimation, adaptive filtering, and so on. For these drawn to sign processing.

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These topics cover a very large territory. In each of these topic areas, numerous volumes have been written. Our intent is to not to provide an exhaustive treatment in each area, but to present enough information to provide a useful set of tools with broad application. Our approach is different from many other books on signal processing, in that we do not exhaustively examine a particular discipline of signal processing-for example, spectrum estimation-bringlng in mathematical tools as necessary to treat isrues that arise.

Given a sequence of observations y[O], y[l], . . , we want to determine, if possible, the parameters of the system. This basic problem has two major variations: The input f [ t ]is deterministic and known. The input f [t ] is random. Other complications may also be modeled in practice. For example, it may be that the output y [t] is corrupted by noise, so that the data available is where w[t] is a noise (or error) signal. This is a "signal plus noise" model that we will employ frequently. In the case where the input is known and there is negligible or no measurement noise, it is straightforward to set up a system of linear equations to determine the system parameters.

X,, are the state variables. bp-1. . , b j ] . 2 1 ) is in state-space form. The system is denoted as (A, b, c T , d ) or, when cl = 0, as (A, b, cT). 21) is called the controller form. The form of the matrix A, with ones above the diagonal and coefficients on the last row, is called a first companion matrix. System transformations; similar matrices The state-variable representation is not unique. In fact, an infinite number of possible realizations exist which are mathematically equivalent, although not necessarily identical in physical operation.

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