y[k] - 1.9*y[k-1] + 0.95*y[k-2] = 0.5*x[k] + 0.3*x[k-1] + 0.2*x[k-2] + 0.4*x[k-3]

Standard Information

• Vairables:
  • x[k] the input at time k
  • y[k] the output at time k
• Difference Equation
  y[k] - 1.9*y[k-1] + 0.95*y[k-2] = 0.5*x[k] + 0.3*x[k-1] + 0.2*x[k-2] + 0.4*x[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] - 1.9*y[k-1] + 0.95*y[k-2] = 0.5*x[k] + 0.3*x[k-1] + 0.2*x[k-2] + 0.4*x[k-3]
  • Ideal input + Noise:
    y[k] - 0.5464*y[k-1] - 0.2331*y[k-2] = 13.014*x[k] - 12.070*x[k-1] + 4.6441*x[k-2] + 1.3194*x[k-3]
• RARX Method Result
  • Ideal input:
    y[k] - 1.9*y[k-1] + 0.95*y[k-2] = 0.5*x[k] + 0.3*x[k-1] + 0.2*x[k-2] + 0.4*x[k-3]
  • Ideal input + Noise:
    y[k] - 0.4163*y[k-1] - 0.2559*y[k-2] = 6.4457*x[k] - 5.4819*x[k-1] + 9.3809*x[k-2] - 3.0173*x[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)