linear time invariant system
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Linear Time Invariant
System
MODUL 3 DAN 4
Sinyal dan Sistem
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Graphical illustration o convolution
properties
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Graphical illustration o convolution
properties
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Dis!rit"
#ontinyu"
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Discrete $onvolution
• $onvolution Throu%h Time &A Graphical Approach'
In this section (e (ill develop a second %raphicalinterpretation o discrete)time convolution* +e (ill ,e%inthis ,y (ritin% the convolution sum allo(in% - to ,e a
causal. len%th)m si%nal and h to ,e a causal. len%th)!. LTIsystem* This %ives us the nite summation.
Notice that or any %iven n (e have a sum o the mproducts o - &l' and a time)delayed h &n ) l'* This is tosay that (e multiply the terms o - ,y the terms o atime)reversed h and add them up*
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$onvolution o continuoussi%nal
• The convolution o ƒ and g is (ritten ƒ /g. usin% an asteris! or star* It isde0ned as the inte%ral o the product
o the t(o unctions ater one isreversed and shited* As such. it is aparticular !ind o inte%ral transorm"
http://en.wikipedia.org/wiki/Asteriskhttp://en.wikipedia.org/wiki/Integral_transformhttp://en.wikipedia.org/wiki/Integral_transformhttp://en.wikipedia.org/wiki/Asterisk
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$onvolution 1rosedure
2* -press each unction in terms o a dummy varia,le *
5* 6e7ect one o the unctions" g&'8g& 9 '*
3* Add a time)o:set. t . (hich allo(s g&t 9 ' to slide alon%the )a-is*
4* Start t at ); and slide it all the (ay to
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$onvolution -ample 2
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$onvolution -ample 5
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