View source for Problem 3 (c) -- Errata

In part (c) of this problem you will have to use as input <math>u(k)=sin(\omega k)</math>, and find the steady state system response. The correct general formula which you should prove is as follows:

<math>M e^{j\theta}=C(e^{j\omega}I-A)^{-1}B + D</math>

Hint: assume that <math>u(k)=sin(\omega k)=\mathcal{I}m(e^{j\omega k})</math>. 

You can therefore find the solution in the required form by using  the Euler formulas: use <math>u(k)=e^{j\omega k}</math>  and  express the general solution of the difference equation as <math>x(k)= G e^{j ...}</math> (you need to figure out this exponent!). 

--[[User:Franco|Elisa]]
[[Category:CDS 101/110 FAQ - Homework 4]]