ece306-8 - ECE 306 -8 Solution of Linear...

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1 Solution of Linear Constant-Coefficient Difference Equations Z. Aliyazicioglu Electrical and Computer Engineering Department Cal Poly Pomona ECE 306 -8 ECE 306-8 2 Solution of Linear Constant-Coefficient Difference Equations Two methods Direct method Indirect Method (z-transform) Direct solution Method: The total solution is the sum of two parts Part 1 homogeneous solution Part 2 particular solution The Homogeneous solution Assuming that the input x(n)=0. Since , this gives us the zero-input response of the system 0 () 0 N k k ayn k = =
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2 ECE 306-8 3 Solution of Linear Constant-Coefficient Difference Equations The solution is the form of an exponential substitute this in the previous equation. The roots can be real or complex or some roots are identical. This is called characteristic polynomial of the system. It has N roots and denotes by () n h yn λ = 12 ( 1 ) 1 ... 0 nn n n N n N NN aa a a λλ −− ++ + + + = ( ) 1 ... 0
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ece306-8 - ECE 306 -8 Solution of Linear...

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