SYDE252 Study Guide - Final Guide: Linear Time-Invariant Theory, Step Function, Convolution

• School: University of Waterloo
• Department: Systems Design Engineering
• Course: SYDE252
• Professor: John Zelek

Document Summary

M order of p(d) (cid:1877)(cid:4666)(cid:1872)(cid:4667)=(cid:1876)(cid:2869)(cid:4666)(cid:1872)(cid:4667) (cid:1876)(cid:2870)(cid:4666)(cid:1872)(cid:4667)= (cid:1876)(cid:2869)(cid:4666)(cid:4667)(cid:1876)(cid:2870)(cid:4666)(cid:1872) (cid:4667)(cid:1856) (cid:1877)[(cid:1863)]=(cid:1876)(cid:2869)[(cid:1863)] (cid:1876)(cid:2870)[(cid:1863)]= (cid:1876)(cid:2869)[(cid:1866)](cid:1876)(cid:2870)[(cid:1863) (cid:1866)] (cid:3041)= . Graphical: flip, start at far left, slide, multiply and add. Remember: a lti system can always be modelled with: (cid:1877)(cid:1872)(cid:4667)= (cid:1876)(cid:4666)(cid:4667) (cid:4666)(cid:1872) (cid:4667)(cid:1856) The output of the filter depends only on the current and previous inputs as well as previous outputs. The impulse response is infinite because there is feedback in the filter; if you put in the(cid:374) (cid:455)i is an infinite number of non-zero values. (cid:3014) (cid:2869) (cid:1877)(cid:3036)= (cid:4666)(cid:1853)(cid:3040) (cid:3040)=(cid:2868) (cid:3015) (cid:2869) (cid:1877)(cid:3041) (cid:3040)(cid:4667) (cid:1854)(cid:3038) (cid:3038)=(cid:2868) (cid:1876)(cid:3041) (cid:3038) Zero input response (continuous), yo(t: let (cid:1843)(cid:4666)(cid:1830)(cid:4667)(cid:1877)(cid:4666)(cid:1872)(cid:4667)=(cid:882) and find characteristic roots (ie sub into: (cid:1877)(cid:3042)(cid:4666)(cid:1872)(cid:4667)=(cid:1829)(cid:2869)(cid:1857)(cid:3117)(cid:3047)+(cid:1829)(cid:2870)(cid:1857)(cid:3118)(cid:3047) . Where d = derivative operator: take derivatives of yo until you have enough equations to solve for all cs (ie take n-1 derivatives (cid:449)here n = # of s(cid:895, use initial conditions given to solve for cs.