y[k] + 0.98*y[k-2] = 5*x[k-1]*w[k-3]

Standard Information

• Vairables:
  • xw[k] the input at time k
    • xw[k] = x[k+2]*w[k];
    • x[k] the first input at time k
    • w[k] the second input at time k
  • y[k] the output at time k
• Difference Equation
  y[k] + 0.98*y[k-2] = 5*x[k-1]*w[k-3]
• Modified Difference Equation
  y[k] + 0.98*y[k-2] = 5*xw[k-3]

First Homework

• MatLab file: hw1.m
• example input: graph
• simulated output: graph
• Ouput with Noise
  • Noise Amplitude: 10% of the maximum value of the output
  • Noise Characteristic: uniform random noise
  • simulated output + noise: graph
• ARX Method Result
  • Ideal input:
    y[k] + 0.98*y[k-2] = 5*xw[k-3]
  • Ideal input + Noise:
    y[k] + 1.0148*10e-2*y[k-1] + 0.9550*y[k-2] = 3.9279*xw[k-3]
• RARX Method Result
  • Ideal input:
    y[k] + 0.98*y[k-2] = 5*xw[k-3]
  • Ideal input + Noise:
    y[k] + 6.0764*10e-3*y[k-1] + 0.9567*y[k-2] = 4.1431*xw[k-3]
• Comparision of the Quality of Parameters (2 Feb 1996)
  • MATLAB file: hw1_e.m
  • Simulated output, graph, from ideal input with
    • the original parameter (yellow)
    • the parameter from ARX method when there is noise (red)
    • the parameter from RARX method when there is noise (green)