(New page: Given: <math>y(t)=x(t)*h(t)=\int_{k=-\infty}^{\infty}x(\tau)h(t-\tau)d\tau</math> #<math>x(t)*(h_1(t)+h_2(t))=\int_{k=-\infty}^{\infty}x(\tau)*(h_1(t-\tau)+h_2(t-\tau)d\tau</math> #<math>...)
 
 
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#<math>x(t)*(h_1(t)+h_2(t))=\int_{k=-\infty}^{\infty}x(\tau)*(h_1(t-\tau)+h_2(t-\tau)d\tau</math>
 
#<math>x(t)*(h_1(t)+h_2(t))=\int_{k=-\infty}^{\infty}x(\tau)*(h_1(t-\tau)+h_2(t-\tau)d\tau</math>
 
#<math>x(t)*(h_1(t)+h_2(t))=\int_{k=-\infty}^{\infty}(x(\tau)*h_1(t-\tau)+x(\tau)*h_2(t-\tau))d\tau</math>
 
#<math>x(t)*(h_1(t)+h_2(t))=\int_{k=-\infty}^{\infty}(x(\tau)*h_1(t-\tau)+x(\tau)*h_2(t-\tau))d\tau</math>
#<math>x(t)*(h_1(t)+h_2(t))=\int_{k=-\infty}^{\infty}x(\tau)*h_1(t-\tau)+\int_{k=-\infty}^{\infty}x(\tau)*h_2(t-\tau)d\tau</math>
+
#<math>x(t)*(h_1(t)+h_2(t))=\int_{k=-\infty}^{\infty}x(\tau)*h_1(t-\tau)d\tau+\int_{k=-\infty}^{\infty}x(\tau)*h_2(t-\tau)d\tau</math>
 
#<math>x(t)*(h_1(t)+h_2(t))=x(t)*h_1(t)+x(t)*h_2(t)</math>
 
#<math>x(t)*(h_1(t)+h_2(t))=x(t)*h_1(t)+x(t)*h_2(t)</math>

Latest revision as of 15:42, 24 June 2008

Given: $ y(t)=x(t)*h(t)=\int_{k=-\infty}^{\infty}x(\tau)h(t-\tau)d\tau $

  1. $ x(t)*(h_1(t)+h_2(t))=\int_{k=-\infty}^{\infty}x(\tau)*(h_1(t-\tau)+h_2(t-\tau)d\tau $
  2. $ x(t)*(h_1(t)+h_2(t))=\int_{k=-\infty}^{\infty}(x(\tau)*h_1(t-\tau)+x(\tau)*h_2(t-\tau))d\tau $
  3. $ x(t)*(h_1(t)+h_2(t))=\int_{k=-\infty}^{\infty}x(\tau)*h_1(t-\tau)d\tau+\int_{k=-\infty}^{\infty}x(\tau)*h_2(t-\tau)d\tau $
  4. $ x(t)*(h_1(t)+h_2(t))=x(t)*h_1(t)+x(t)*h_2(t) $

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