Signal Processing y(t) System G{x(} Input Output signal signal Transfer function ( filter) Allow certain frequency band to pass, and reject others Figure 1
x(t) System y(t) = G{x(t)} Input signal Transfer function (filter) Allow certain frequency band to pass, and reject others Output signal Figure 1 Signal Processing
Signal Processing y(t) hr(0) G{x(} Input Output signal signal Non-recursive system hr(0) Feed forward response Figure 2
x(t) Input signal Non-recursive system Output signal hFF(t) hFF(t) Feed forward response y(t) = G{x(t)} Figure 2 Signal Processing
Signal Processing y() x() hr(0) G{() Input Output signal signal Non-recursive system y()=x(0)hF(0 (1) Igure 3
x(t) Input signal Non-recursive system Output signal hFF(t) y(t) = x(t) * hFF(t) (1) y(t) = G{x(t)} Figure 3 Signal Processing
Convolution=x(0)*h(=y(0=]moxt-rdr h(t) x(t) 2-10123456 -2-10123456 y(O)=AREAh(r)x(T) →r 5-4-3-2-10123456 y(1)=AREAh(t)(x(1-t 5-4-3-2-10123456
Convolution y(t) = x(t) * h (t) -2 -1 0 1 2 3 4 5 6 h( ) -2 -1 0 1 2 3 4 5 6 x( ) -2 -1 0 1 2 3 4 5 6 y(0)= AREA[h( ) x(- )] -5 -4 -3 = ( ) ( − ) − y(t) h x t d -2 -1 0 1 2 3 4 5 6 y(1)= AREA[h( ) x(1- )] -5 -4 -3
Convolution=x(0)*h(=y(0=]moxt-rdr h(t) x(t) 2-10123456 2-10123456 (2)=AREA()∩x2) →r -5-4-3-2-10123456 y(3)=AREAh()x(3-T) 5-4-3-2-10123456
Convolution y(t) = x(t) * h (t) -2 -1 0 1 2 3 4 5 6 h( ) -2 -1 0 1 2 3 4 5 6 x( ) -2 -1 0 1 2 3 4 5 6 y(2)= AREA[h( ) x(2- )] -5 -4 -3 = ( ) ( − ) − y(t) h x t d -2 -1 0 1 2 3 4 5 6 y(3)= AREA[h( ) x(3- )] -5 -4 -3