a b We will use xt xn to refer to CT and DT signals respectively Slide 18

# A b we will use xt xn to refer to ct and dt signals

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(a). (b). We will use x(t), x[n] to refer to CT and DT signals respectively.

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Slide 18 CUHK(SZ) EIE 3001, Spring 2018/19 Infinite Duration Signal and Finite Duration Signal a If a signal lasts for such a long time that we can regard it as lasting forever, we say it is of infinite duration . a If a signal last only for a finite period of time, we say that it is of finite duration . a A finite duration signal could be one segment of a longer duration signal that we extract and process at a time.
Slide 19 CUHK(SZ) EIE 3001, Spring 2018/19 CT and DT System a A system that processes CT signals is a Continuous-Time (CT) System . a A system that processes DT signals is a Discrete-Time (DT) System .

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Slide 20 CUHK(SZ) EIE 3001, Spring 2018/19 Variable Transformation
Slide 21 CUHK(SZ) EIE 3001, Spring 2018/19 DT Signal as Vector a A finite duration DT signal is a sequence of N complex numbers. Therefore it can be represented by a complex N -vector.

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Slide 22 CUHK(SZ) EIE 3001, Spring 2018/19 Basic Manipulation of Signals a CT and DT signals x(t) , x[n], are just functions of time. The most basic way that we can manipulate a signals is to multiply it by a constant.
Slide 23 CUHK(SZ) EIE 3001, Spring 2018/19

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Slide 24 CUHK(SZ) EIE 3001, Spring 2018/19 Transformation of Independent Variable
Slide 25 CUHK(SZ) EIE 3001, Spring 2018/19 Transformation of independent variable (cont.) (3a). Time shift

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Slide 26 CUHK(SZ) EIE 3001, Spring 2018/19 Transformation of Independent Variable (cont.) a (3b). Time Reflection (or Time Reversal) x(t) x(-t) x[n] x[-n] x( t ) t x[ n ] n y(n)=x[- n ] n t y(t)=x(- t )
Slide 27 CUHK(SZ) EIE 3001, Spring 2018/19 Transformation of Independent Variable (cont.) a (3c). Time Scaling x 1 (t) x( α t)

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Slide 28 CUHK(SZ) EIE 3001, Spring 2018/19 Transformation of independent variable (cont.) x( t ) 1 2 t x( t+ 1) -1 1 2 t -2/3 2/3 x(1.5 t+ 1) 1 2 t To perform transformation x(t) o x( D t+ You have to do time-shifting then scaling .
Slide 29 CUHK(SZ) EIE 3001, Spring 2018/19 Combination of Shifting and Scaling

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Slide 30 CUHK(SZ) EIE 3001, Spring 2018/19
Slide 31 CUHK(SZ) EIE 3001, Spring 2018/19 Even and Odd functions a A signal is called an even signal (function) if a A signal is called an odd signal (function) if x(t) = - x(-t) x[n] = - x[-n] x(t) = x(-t) x[n] = x[-n]

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Slide 32 CUHK(SZ) EIE 3001, Spring 2018/19 Even and Odd functions -10 -8 -6 -4 -2 0 2 4 6 8 10 -1 -0.5 0 0.5 1 t sin(t) -10 -8 -6 -4 -2 0 2 4 6 8 10 -1 -0.5 0 0.5 1 t cos(t)
Slide 33 CUHK(SZ) EIE 3001, Spring 2018/19

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