The document discusses the NLMS adaptive filter algorithm. The LMS algorithm adjusts the coefficients of a filter to minimize the mean square error between the desired and actual output signals. The NLMS algorithm normalizes the step-size parameter based on the input signal power to overcome issues from changing input power levels. A result is shown comparing actual and estimated filter weights using the NLMS algorithm.

1. NLMS Algorithm for adaptive
filter
DSP lab-Mini Project
Chintan Joshi

2. LMS Filter
• Adjusts the coefficients of w(n) of a filter in
order to reduce the mean square error
between the desired signal and output of the
filter.
• Algorithm use the gradient vector of the filter
tap weights
• w(n +1) = w(n) +μe(n)x* (n)

3. NLMS Adaptive Filter
• In real Scenario, input signal power not remain
constant
– change the step-size between two adjacent
coefficients of the filter will also change
– affect the convergence rate
– gradient noise amplification problem
• To overcome this problem, adjust the step-size
parameter with respect to the input signal power
• Therefore the step-size parameter is said to be
normalized

4. NLMS Adaptive Filter cont..

5. Result
Comparison of the actual weights and the estimated weights
0.5
Actual weights
0.4 Estimated weights
0.3
0.2
0.1
0
-0.1
-0.2
-0.3
-0.4
-0.5
0 1 2 3 4 5 6