ece306-5 - 1 && ECE 306...

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Unformatted text preview: 1 && ECE 306 Discrete-Time Signals and Systems & && && Addition, Multiplication, and Scaling of Sequences Amplitude Scaling: (A Constant Multiplier) ( ) ( ), y n Ax n n =- < < x(n) A y(n)=Ax(n) Addition of two signals (An Adder) 1 2 ( ) ( ) ( ), y n x n x n n = +- < < + x 1 (n) y(n)=x 1 (n)+ x 2 (n) x 2 (n) 2 && Addition, Multiplication, and Scaling of Sequences The product of two signals (A signal Multiplier) A unit delay element A unit advance element 1 2 ( ) ( ) ( ), y n x n x n n =- < < x x 1 (n) x 2 (n) y(n)=x 1 (n) x 2 (n) z-1 x(n) y(n)=x(n-1) z x(n) y(n)=x(n+1) && Input-Output Description of Systems The relation between the input and output signals are known input- output relationship Mathematical representation of the transformation is Discrete- time System x(n) y(n) Output signal or response input signal or excitation denotes the transformation. In general input-output relationship can be also shown as [ ] ( ) ( ) y n x n = ( ) ( ) x n y n 3 && Input-Output Description of Systems The input signal is Example: 3 3 ( ) otherwise n n x n &- = ( ) ( ) y n x n = ( ) ( 1) y n x n =- ( ) ( 1) y n x n = + [ ] 1 ( ) ( 1) ( ) ( 1) 3 y n x n x n x n = + + +- [ ] ( ) max ( 1), ( ), ( 1) y n x n x n x n = +- ( ) ( ) ( ) ( 1) ( 2) ... n k y n x k x n x n x n =- = = +- +- + a b c d e f Solution { } ( ) ...,0,3,2,1,0,1,2,3,0,... x n = ( ) ( ) y n x n = { } ( ) ...,0,3,2,1,0,1,2,3,0,... y n = a ( ) ( 1) y n x n =- { } ( ) ...,0,3,2,1,0,1,2,3,0,... y n = b && Input-Output Description of Systems Solution (cont) ( ) ( 1) y n x n = + { } ( ) ...,0,3,2,1,0,1,2,3,0,... y n = c d f [ ] 1 ( ) ( 1) ( ) ( 1) 3 y n x n x n x n = + + +- [ ] [ ] 1 1 2 (0) (1)...
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This note was uploaded on 03/11/2008 for the course ECE 306 taught by Professor Aliyazicioglu during the Winter '08 term at Cal Poly Pomona.

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ece306-5 - 1 && ECE 306...

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