convolution - 19.1 19. CONVOLUTION 19.1 INTRODUCTION • Can be used to find normal input reponses for linear systems • It is most useful for finding an output response for a system given an arbitrary input function • It is also the basis for other methods that come later for system analysis. 19.2 UNIT IMPULSE FUNCTIONS • A unit impulse function Topics: Objectives: convolution - 19.2 • For a unit step function, • If we look at an input signal (force here) we can break it into very small segments in time. As the time becomes small we can approximate it with a set of impulses. 1ε -- ε t Area ε 1ε -- = =1 Unit impulse t δ(t) P(t) ε →0 = lim Area δ(t)dt –∞ ∞ =∫ =1 Dirac delta function P(t) This function is theoretically undefined, it goes to infinity for an instant, but it does have an area of 1. 0 u(t
