CH1 Signals Part 2

CH1 Signals Part 2 - EE 3120 Chapter 1 Lecture 3...

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EE 3120 Chapter 1 Lecture 3 Manipulation of Signals in Time
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Manipulation of Signals in time We can manipulate signals many different ways – first steps in signal processing Shifting f(t) = sin(t) f(t-T) shifting right T seconds f(t+T) shifting left T seconds f(t-T) = sin(t-T) f(t) = sin(t+T)
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Manipulation of Signals in time Flipping or Reversing f(t) f(-t) f(t) f(-t) f(2) = 2 ; for t = 2 f(-2) = 2 ; for t = 2
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Manipulation of Signals in time Flipping and shifting T = 2 T = 3 f(t) same as flipping f(t+T) Æ shift and flip f(-t +T) f(-t-T)
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Manipulation of Signals in time Addition f(t) h(t) Two signals f(t) and h(t) defined for all t. Their sum h(t) + f(t) forms a new signal where the sum is addition point by point at every t. f(t) + h(t)
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Manipulation of Signals in time Multiplication by h(t) h(t) = constant c scaling : c > 1 is amplification ; 0 < c < 1 is attenuation if c < 0 then f(t) is also inverted h(t) = u(t) the unit step function Æ truncation, u(t) truncates the negative-time part of f(t) f+(t) = f(t)u(t) f-(t) = f(t)u(-t) h(t) = p a( t ) : = 0 for t < - a 1 for -a t a the rectangular pulse 0 for t > a Multiplication of p a (t) is called windowing because f(t) remains between the window from [–a a ] after multiplication (like looking through a window)
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CH1 Signals Part 2 - EE 3120 Chapter 1 Lecture 3...

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