Unformatted text preview: x 1 [ n ] x 2 [ n ] x 3 [ n ] , and two outputs y [ n ] = ± y 1 [ n ] y 2 [ n ] ² , that satisfy the equation ± 1 1 1 1 1 ² x [ n ] = y [ n ] + ± 1 ² y [ n-1] . (a) Find an explicit expression for the impulse response of the system. (b) Find the output when the input of the system is x [ n ] = δ [ n ] u [ n ] , where u [ n ] = 0 if n < 0 and u [ n ] = 1 if n ≥ 0. (c) Can you ﬁnd two distinct sets of three input signals that give rise to the same two output signals? 4. A square matrix L is said to be lower triangular if L i,j = 0 when i < j . Show that the product of two lower triangular matrices is another lower triangular matrix. 5. Do problems 1.3.6, 1.4.10, 1.4.20, 1.4.22, and 1.4.24 from the textbook....
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- Summer '10
- Matrices, Characteristic polynomial, Triangular matrix