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## 10.3 Wiener Filtering

### 10.3.1 Concept of Minimum Mean-Square-Error Estimation

Wiener filtering is a classical method of optimal estimation of the original signal x( t) or { x n} based on the measured (observed) signal y( t), { y n} in the presence of stochastic noise ?( t), { ? x}. The noise component precludes the precise restoration of the original and therefore we have to be satisfied with only an approximate estimation or { } which would be optimal in a suitably defined sense.

The task is, in its most general form, formulated using the concept that both the original signal and noise, and consequently even the observed signal as derived via the distortion model, are realisations of stochastic processes. Then we can interpret these signals as members of function families or { }, or { }, or { } and the equations, which we shall deal with in the following paragraphs, therefore as members of families of equations where every member applies to a particular combination of realisations.

The criterion of optimality is based on the notion of the error signal or { }; even this signal is, of course, stochastic and all its possible realisations form the family or { }. The Wiener restoration considers as the optimum restoration such an approach that, when applied to all possible combinations of the mentioned process realisations, leads to such estimates that their ensemble mean...

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Data acquisition is the digitizing and processing of multiple sensor or signal inputs for the purpose of monitoring, analyzing and/or controlling systems and processes. Signal conditioning includes the amplification, filtering, converting, and other processes required to make sensor output suitable for rereading by computer boards.
Noise Figure Meters
RF noise figure meters measure the noise contribution of an amplifier relative to a noise-free amplifier at a reference temperature. Usually expressed in dB for Ku-band amplifiers.
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##### Topics of Interest

10.4 Kalman Filtering 10.4.1 Introduction A Kalman filter may be considered as a generalisation of the Wiener filter in two directions. Primarily, it does not require stationarity of the...

10.7 Generalised Discrete Mean-Square-Error Minimisation The method that we shall introduce in this section is, in a sense a generalisation of Wiener filtering. The concept assumes that both the...

Wiener Filters   2.0 INTRODUCTION Wiener filters are best linear least squares filters which are used for prediction, estimation, interpolation, signal and noise filtering, and so forth. To...

11.1 Concept of Adaptive Filtering In the previous chapter, when designing restoration filters which should provide optimal estimates of original signals based on their observed noisy and distorted...

In this chapter methods of Stochastic Calculus are applied to the Filtering problem in Engineering and Random Oscillators in Physics. The Filtering problem consists of finding the best estimator of a...

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