Prove The update rule w(n + 1) = w(n) + µe(n)x(n) It's the update rule, a fundamental expression in the Least Mean Squares (LMS) adaptive filter algorithm Note: w(n): The filter coefficients in iteration n. μ: The learning rate, which controls the convergence speed of the algorithm. It's a parameter that is adjusted according to the problem and conditions. • e(n): The error in iteration n, which is the difference between the desired output and the estimated output in that iteration. x(n): The input signal in iteration 7, which is the signal being filtered using the coefficients w to produce the estimated output.

Prove The update rule w(n + 1) = w(n) + µe(n)x(n) It's the update rule, a fundamental expression in the Least Mean Squares (LMS) adaptive filter algorithm Note: w(n): The filter coefficients in iteration n. μ: The learning rate, which controls the convergence speed of the algorithm. It's a parameter that is adjusted according to the problem and conditions. • e(n): The error in iteration n, which is the difference between the desired output and the estimated output in that iteration. x(n): The input signal in iteration 7, which is the signal being filtered using the coefficients w to produce the estimated output.