Fixed and adaptive - optimal filtering, Electrical Engineering

Optimal Filtering

1389_Fixed and Adaptive.png

A system identi?cation structure is shown in Figure 1. The discrete-time signal [ ] forms the input to an unknown system represented by a moving average, FIR, ?lter with parameters, {ω01 ωn} . The output of the unknown system is given by

466_Fixed and Adaptive1.png

This can be represented more concisely in vector notation as

1891_Fixed and Adaptive2.png

where ω and x[k] are Nw + 1 element column vectors, underlines are used to denote vector quantities and the superscript (·)T represents a vector transpose.

A noise signal n[k] is added at the output of the system to yield a realistic measured output signal z[k]. An optimum ?lter is to be designed which operates on the input signal x[k] and measured output signal z[k] to yield the closest match to the unknown system. The optimum ?lter is assumed to be a moving average ?lter with the same number of parameters as the unknown system, i.e. opt.

This problem arises in many applications, for example control of some machinery plant, or of acoustic and electrical echoes in telecommunications. The Wiener solution is found by minimising the mean-square error between z[k] and y[k], where y[k] is the output of the optimum ?lter driven by x[k]. The circum?ex is used to denote that the output of the optimum ?lter is an estimate of the output of the unknown system.

If x[k]and n[k] are assumed to be uncorrelated stationary random discrete signals then the mean square error is de?ned as

2274_Fixed and Adaptive3.png

where {·} is the statistical expectation operation, which to a ?rst approximation can be considered to be an average. The right hand side of equation (1) contains a vector of crosscorrelation components and a matrix of autocorrelation components, i.e.

555_Fixed and Adaptive4.png

Differenting equation (1) with respect to opt and setting the result to zero yields the optimum Wiener ?lter solution which is given by

596_Fixed and Adaptive5.png

Posted Date: 2/27/2013 6:32:29 AM | Location : United States







Related Discussions:- Fixed and adaptive - optimal filtering, Assignment Help, Ask Question on Fixed and adaptive - optimal filtering, Get Answer, Expert's Help, Fixed and adaptive - optimal filtering Discussions

Write discussion on Fixed and adaptive - optimal filtering
Your posts are moderated
Related Questions
2. A 6 pole lap-wound armature having 720 conductors, rotates in a field of 20.35 mWb. (a) If the induced current is 72 A, what is the torque developed by armature? (b) If the indu

The magnetic fields can be plot by using: i.  Compass ii.  Iron dust method  .

I want project ideas.

Consider the circuit of Figure (a) and obtain the complete solution for the voltage v C (t) across the 5-F capacitor and the voltage v x (t) across the 5- resistor.

Q. Three waveforms seen on an oscilloscope are shown in Figure. If the horizontal scale is set to 50 ms per division (500 ms for the entire screen width), and the vertical scale is

Q. Illustrate Power Semiconductor Devices? Since the advent of the first thyristor or silicon-controlled rectifier (SCR) in 1957, tremendous advances have been made in power se

advantages and disadvantages of thevenin theorem

Q. Radiation intensity pattern of Antennas? Antennas do not radiate power equally in all directions in space. The radiation intensity pattern describes the power intensity (whi

Case 2 ( A>B) Suppose XX = 05H ( stored  in A ) And  YY = 02H ( stored  in B). Then carry  flag will  reset by CMP instruction, since  A> B in this  case JNC  will transfer the

show a schematic diagram of michelson interferometer