This document discusses convolution and its applications in signal processing. Convolution combines two signals to form a third signal. For discrete time signals, convolution is known as the convolution sum, which can be found using sequence, graphical, or tabulation methods. For continuous time signals, convolution is represented as a convolution integral. Convolution is useful for determining the output of a linear time-invariant system given its impulse response. It also independently amplifies or attenuates frequency components of the input signal. Convolution filtering is important for algorithms in digital image processing like edge detection.

1. SUB : SIGNALS AND SYSTEMS
TOPIC : LTI SYSTEM
MADE BY : KIRTI .H. MANDAL
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2. TABLE OF CONTENT
1. Response of continuous time LTI system
2. Convolution of CT signal
3. Response of DT LTI system
4. Convolution of DT signal
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3. CONVOLUTION
• Convolution is the most important and fundamental concept in signal
processing and analysis . By using convolution, we can construct the
output of system for any arbitrary input signal, if we know the impulse
response of system.
• How is it possible that knowing only impulse response of system can
determine the output for any given input signal ? We will find out the
meaning of convolution.
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4. CONVOLUTION
• Convolution is a mathematical way of combining two signals to form a
third signal.
• Convolution is a formal mathematical operation , just as multiplication
,addition ,and integration . Addition takes two numbers and produces a
third number , while convolution takes two signals and produces a third
signal .
• The steps to be taken to find the convolution of two signals are as follow:
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5. CONVOLUTION
 First,the input signal can be decomposed
into a set of impulse, each of which can be
viewed as a scaled and shifted delta
function.
 Second, the output resulting from each
impulse is a scaled and shifted version of
the impulse response.
 Third, the overall output signal can be
found by adding these scaled and shifted
impulse response.
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6. CONVOLUTION FOR DT SIGNAL
Convolution for discrete time signal is known as convolution sum.
the convolution sum is represented as shown below :
We have three methods to find convolution sum :
1. Sequence method
2. Graphical method
3. Tabulation method
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7. CONVOLUTION FOR CT SIGNAL
• Convolution for continuous time signal is also known as convolution
integral.
• And it is represented as shown below :
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8. APPLICATIONS
• In digital signal processing and image processing applications , the entire
input function is often available for computing every sample of the
output function.
• Convolution amplifies or attenuates each frequency component of the
input independantly of the other components .
• In digital image processing , convolution filtering plays an important role
in many important algorithms in edge detection and related processes.
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