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Impulse_function-1

# Impulse_function-1 - Connexions module m10059 1 The Impulse...

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Unformatted text preview: Connexions module: m10059 1 The Impulse Function * Melissa Selik Richard Baraniuk This work is produced by The Connexions Project and licensed under the Creative Commons Attribution License † Abstract Explains the use of the unit impulse function. In engineering, we often deal with the idea of an action occurring at a point. Whether it be a force at a point in space or a signal at a point in time, it becomes worth while to develop some way of quantitatively de ning this. This leads us to the idea of a unit impulse, probably the second most important function, next to the complex exponential 1 , in systems and signals course. 1 Dirac Delta Function The Dirac Delta function , often referred to as the unit impulse or delta function, is the function that de nes the idea of a unit impulse. This function is one that is in nitesimally narrow, in nitely tall, yet integrates to unity , one (see (1) below). Perhaps the simplest way to visualize this is as a rectangular pulse from a- 2 to a + 2 with a height of 1 . As we take the limit of this, lim → , we see that the width tends to zero and the height tends to in nity as the total area remains constant at one. The impulse function is often written as δ ( t ) . Z ∞-∞ δ ( t ) dt = 1 (1) * Version 2.20: Sep 28, 2009 3:59 pm GMT-5 † http://creativecommons.org/licenses/by/1.0 1 "The Complex Exponential" <http://cnx.org/content/m10060/latest/> http://cnx.org/content/m10059/2.20/ Connexions module: m10059...
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Impulse_function-1 - Connexions module m10059 1 The Impulse...

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