LMS-2 - LMS Algorithm: Motivation LMS Only a single...

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LMS Algorithm: Motivation LMS Algorithm: Motivation ± Only a single realization of observations available. ± Statistics need to be estimated. ± Need to estimate the gradient vector ± Elaborate estimation : delay in tap-weight adjustment. ± Simplicity: real-time applications possible. LMS Algorithm LMS Algorithm ± Use instantaneous estimates for statistics: ± Filter output: ± Estimation error: ± Tap-weight update: LMS Algorithm LMS Algorithm ± Estimate of gradient used: ± Estimate of gradient unbiased: ± Gradient estimate contains gradient noise: ± Tap-weight converges in the mean : LMS Algorithm LMS Algorithm ± Given w[0] = 0 for the LMS filter: ± Input-output relation nonlinear: ± Feedback in recursive tap-weight update makes stability considerations important.
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LMS : Independence Theory LMS : Independence Theory ± Tap inputs u[n] comprised of statistically independent random vectors. ± Tap inputs u[n] independent of previous samples of
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LMS-2 - LMS Algorithm: Motivation LMS Only a single...

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