Net 222: Communications and networks fundamentals ( Practical Part)
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NET 222: COMMUNICATIONS AND NETWORKS FUNDAMENTALS (PRACTICAL PART) Tutorial 5 : Matlab – Aljabric equations. – convolution Networks and Communication Department 1
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Net 222: Communications and networks fundamentals ( Practical Part). Tutorial 5 : Matlab – Aljabric equations. – convolution. Lecture Contents. Solving Algebraic equations: Simple equations. Quadratic equations. Plotting Symbolic Equations. Computing derivatives. Integration. - PowerPoint PPT Presentation
Transcript of Net 222: Communications and networks fundamentals ( Practical Part)
NET 222: COMMUNICATIONS AND NETWORKS FUNDAMENTALS (PRACTICAL PART)Tutorial 5 : Matlab – Aljabric equations. – convolution
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Lecture Contents
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Solving Algebraic equations: Simple equations. Quadratic equations. Plotting Symbolic Equations. Computing derivatives. Integration.
Convolution.
Simple equations3
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Example
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Solve : x+5=0
Quadratic equations5
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Example
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Solve :
Plotting Symbolic Equations7
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Example 1:
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Example 2:
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Computing derivatives10
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Example
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Find the derivative for :
f = sin(5*x)
Integration12
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Example 1:
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Find the integration for x^2 :
Example 2:
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Convolution15
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Convolution Sum
The Convolution sum:The equation below defines the convolution of two sequences and denoted by:
(The convolution sum or superposition sum)
And the operation on the right hand side (equation in bold ) is known as the convolution of the sequence and h.
It is commonly called the convolution sum. Thus, again, we have the fundamental result that the output of any discrete-time LTI system is the convolution of the input with the impulse response of the system.
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Convolution Sum (Cont.)
The Figure below illustrates the definition of the impulse response h[n] and the relationship of
Example
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Consider an LTI system with impulse response h[n] and input x[n].
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Any Questions ?
The End
