For a CT ramp signal is designated by rt and mathematically defined as t t t t

For a ct ramp signal is designated by rt and

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For a C.T. ramp signal is designated by r(t) and mathematically defined as 0 0 0 ) ( t t t t r Graphical representation We can also express r(t)in terms of u(t) as r(t)=t·u(t). d u t r t ) ( ) ( ) ( ) ( t r dt d t u
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DT Unit ramp signal Similarly the DT ramp signal can be defined as Graphical representation Representation of DT ramp in terms of u[n] 0 0 0 ) ( n n n n r And DT unit step in terms of ramp can written as  n k k u n r ) ( ) ( ) ( ) 1 ( ) ( n r n r n u
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Unit impulse (sample) signal An Impulse function is having important role in signal analysis. Continuous time unit impulse function also known as Dirac delta function was first defined by Dirac as (t)=1 for t 0 and 1 ) ( dt t An impulse function (t) is a pulse defined about t=0, which covers 1 unit area about the origin. It is a delicate concept to represent impulse graphically see the figures in next slide where the impulse function is represented graphically.
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Unit impulse (sample) signal Graphical representation Therefore the shape of the signal doesn’t matter, if area covered by pulse about the origin is 1 then it is called as impulse function (t). Generally it is represented by arrow at t=0 for CT signal as shown in fig 1.30 (c) with strength equals to 1.
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Unit impulse (sample) signal If width of the impulse gradually approaches to zero then amplitude of impulse will go on increasing and at width equal to 0 the amplitude will be infinite. That is impulse at 0 has infinite amplitude. The impulse function is a derivative of unit step function or we can say unit step function is a integration of unit impulse function. d t u t ) ( ) ( ) ( ) ( t u dt d t
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Properties of impulse signal The reflection of impulse is impulse itself. This property of impulse response is termed as reflection property of impulse response. Time scaling property ) ( ) ( t t ) ( ) ( at a t Time shift property: Shall be covered after studying basic operations on signals
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DT Unit impulse (sample) signal Discrete version of unit impulse signal is easier to understand which can be defined as Graphical representation 0 0 0 1 ) ( n n n Every signal shall be expressed in terms of unit sample sequence(signal)
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Rectangular pulse Definition Graphical representation otherwise t t 0 1 ) ( 2 1
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Triangular Pulse Definition Graphical representation a t a t t a t a 0 1 ) ( x (t) t a - a 1
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Signum Function Definition Graphical representation a t a t t a t a 0 1 ) ( x (t) t 1 -1
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Sinc Pulse Definition Graphical representation t t t Sin t Sinc ) ( ) ( The Sinc function oscillates with period 2 and decays with increasing t. It’s value is zero at n .
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Revise the elementary signals studied Exponential signal Sinusoidal signal Unit step signal Unit ramp signal Unit impulse (sample) signal Rectangular pulse Triangular pulse Signum function Sinc function
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Basic operations on signals Whenever we need to perform any operation on the signal either amplitude or time variable of the signal will be modified.
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