Basics of LTI systems

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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