lecture 2

lecture 2 - EE 3120 Linear Systems Analysis Lecture 2...

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EE 3120 Linear Systems Analysis Lecture 2 Manipulation of Continuous and Discrete time Signals reference time, the time we start to study the signal that depends on whether you are a mathematician or an engineer What is t = 0 ? What is t Æ ? Let’s consider the real exponential function: f(t) = e at for a < 0 for t Æ , f(t) Æ 0 but… for at = -5, f(t) = 0.007 after 5 time constants, f(t) is less than 1% of the original value at f(0) = 1. Is this small enough to be considered infinity? In many controls and filter applications, YES. So… if f(t) = e -0.1t ; f(t) Æ 0 at 50 seconds (5 time constants); = 50 second if f(t) = e -5t ; f(t) Æ 0 at 1 second (5 tiem constants); = 1 second hmmm…. .
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EE 3120 Linear Systems Analysis Lecture 2 Manipulation of Continuous and Discrete time Signals Positive time signals f(t) = 0 for t < 0 f(t) = f + (t) Negative time signals f(t) = 0 for t > 0 f(t) = f - (t) 2-sided signals f(t) 0 for any t < 0 and t > 0 Most signals in practice are positive time signals. Boundedness
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lecture 2 - EE 3120 Linear Systems Analysis Lecture 2...

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