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lecture 20

# lecture 20 - Summary of Lecture#20(t Convolution integral 0...

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1 1 Summary of Lecture #20 10/08/2010 Convolution integral Flip, shift, multiply and integrate Key properties of convolution integrals Evaluate convolution integrals- Examples Properties of Delta function, δ (t), a review Convolution with Delta function Graphical convolution- examples - - τ τ - τ = τ τ τ - = = d ) t ( h ) ( f d ) ( h ) t ( f ) t ( h ) t ( f ) t ( y 2 h(t) δ (t) 0 h(t) h(t) δ (t-t 0 ) 0 h(t-t 0 ) h(t) a δ (t-t 1 ) 0 a h(t-t 1 ) t 1 >0 h(t) b δ (t-t 2 ) 0 t 2 <0 b h(t-t 2 ) h(t) 0 h(t) 0 1 2 b (t t ) I a (t t ) nput (t) = + δ + - δ δ - 2 1 bh(t t ) Output h(t ah(t ) t ) = + + - - - δ = ) t t ( ) t ( f Input j j - = ) t t ( h ) t ( f Output j j 3 Flip, shift, multiply and integrate Flip and shift one of the two functions. Which one to flip and shift? Either one will do. In the flipped and shifted function, replace τ by t - τ Multiplication Integrate from - ∞ to + ∞. h(t) f(t) y(t) = ? f(t): Input signal h(t): Impulse response y(t): Output signal y(t) f(t )h( )d f( )h(t )d f(t) h(t) h(t)*f(t) -∞ -∞ - τ τ τ = τ - τ τ = = 4 h( ) h( τ ) h(t ) f( τ ) b a b t h( τ ) Time reversal flip, h( )

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lecture 20 - Summary of Lecture#20(t Convolution integral 0...

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