Figures for bsp

Simulation Results and Observations

Part 1: Time-delay Estimation Problem:

A: When x(n) = -0.6*x(n-1) + w(n):

LMS Algorithm:

Observation: The estimators converges to a value near to true value.

Observation: The graph exponentially decreases to a value near to zero.

NLMS Algorithm:

Observation: The values are neaarly converged.

Observation: Initially increased to a value 2.98 and become constant at 1.19.

RLS Algorithm:

Observation: Nearly converges to true values.

Observation: Initially increased to 2.02 and stays constant at 1.009.

Observation: Converges to a value 0.45.

B: When x(n) = 4*sin(2*pi*n/17) and (n) = 0:

LMS Algorithm:

Observation: Exactly converges to true values.

Observation: nearly converges to zero.

NLMS Algorithm:

Observation: Exactly converges to true value.

Observation: nearly converged to zero.

RLS Algorithm:

Observation: Exactly converges to the true values.

Observation: converged to zero.

Observation: Converged to zero.

Part 2: Noise Cancellation Problem:

LMS Algorithm:

Observation: Approximatly converging to true value but fluctuating.

Observation: Initially increased to 60 and stays constant at 58.

Observation: Fluctuates between -20 and 20.

Observation: Fluctuates between -12 and 12.

RLS Algorithm:

Observation: Converges nearly to true values.

Observation: Initially increases to 61 and stays constant at 51.2

Observation: Fluctuates at 2.5

Observation: Fluctuates between -20 and 20.

Observation: Fluctuates between -10 and 10.

Part 3: Noise Cancellation Problem:

LMS Algorithm:

Observation: Nearly converged to true values.

Observation: Exponentially decreased to 0.2

Observation: Fluctuates between -6 and 6

Observation: Converges neaarly to zero.

NLMS Algorithm:

Observation: Converges nearly to true values.

Observation: Initially increased to 16.3 and reduces to 6.1

Observation: Fluctuates to different values between -5 to 5.

Observation: Fluctuates between -3 and 3.

RLS Algorithm:

Observation: Converges to exact values.

Observation: Converges to zero.

Observation: Fluctuates between -7 and 7.

Observation: Converged to zero.

Observation: Nearly equal to 0.5

Part 4: RLS-Identification Problem:

A:

Observation: Exactly converged to true values.

Observation: Converged to zero.

Observation: Converged to zero.

B:

Observation: Nearly converged to true value.

Observation: Converged to 1.

Observation: Converged to 0.2

C:

Observation: Exactly converged to true values.

Observation: Converged to zero.

Observation: Converged to zero.

Part 5:

LMS Algorithm:

Observation: Converged to -3.6 which is near to true value -3.5

NLMS Algorithm:

Observation: Converged to -3.4 which is near to true value -3.5

RLS Algorithm:

Observation: Converged to -3.44 which is near to true value -3.5