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categoryالهندسة الكهربائية schoolبكالوريوس event_available2026-07-15

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3.4 In a variant of the LMS algorithm called the leaky LMS algorithm, the cost function to be minimized is defined by 1 (n) = \e(n) + (n) where w(n) is the parameter vector, e(n) is the estimation error, and λ is a constant. As in the ordinary LMS algorithm, we have e(n) = d(n) − w²(n)x(n) where d(n) is the desired response corresponding to the input vector x(n). (a) Show that the time update for the parameter vector of the leaky LMS algorithm is defined by - ŵ(n + 1) = (1 − yλ)ŵ(n) + mx(n)e(n) which includes the ordinary LMS algorithm as a special case.

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