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Programming Assignments

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Introduction   ::   System Model   ::   Expectation   ::   Part 1   ::   Filters   ::   Part 2   ::   Submission

Programming Assignment Part 1

The file sysid1 on the class website contains input/output data for an unknown system. The first column contains input $ u(t)$ ; the second column contains output $ y(t)$ . It is known that the filter has five coefficients,

$\displaystyle G(z) = g_0 + g_1 z^{-1} + g_2 z^{-2} + g_3 z^{-3} + g_4 z^{-4}
$

(that is, $ L_g = 4$ ) and the AR process has

$\displaystyle H^{-1}(z) = 1 + a_1 z^{-1} + a_2 z^{-2} + a_3 z^{-3}
$

(that is, $ L_h = 3$ ).

Write a M ATLAB program that reads in the data and, using the iterative procedure outlined in section 2.2.3, estimates $ G(z)$ and $ H^{-1}(z)$ . Also, determine an estimate for $ \sigma_e^2$ .

Hints:

  • You are strongly encouraged to choose your own $ G(z)$ and $ H^{-1}(z)$ filters and create your own input/output data for debugging purposes. You can verify that your program correctly identifies the parameters in your simulated system, then use your program on the unknown data.
  • Helpful M ATLAB commands: filter , rand , randn .
Copyright 2008, by the Contributing Authors. Cite/attribute Resource . admin. (2006, June 13). Programming Assignments. Retrieved January 07, 2011, from Free Online Course Materials — USU OpenCourseWare Web site: http://ocw.usu.edu/Electrical_and_Computer_Engineering/Stochastic_Processes/sysid_4.htm. This work is licensed under a Creative Commons License Creative Commons License