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Net 222: Communications and networks fundamentals ( Practical Part)

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.

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Net 222: Communications and networks fundamentals ( Practical Part)

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  1. Net 222: Communications and networks fundamentals (Practical Part) Tutorial 5 : Matlab – Aljabric equations. – convolution Networks and Communication Department

  2. Lecture Contents • Solving Algebraic equations: • Simple equations. • Quadratic equations. • Plotting Symbolic Equations. • Computing derivatives. • Integration. • Convolution. Networks and Communication Department

  3. Simple equations Networks and Communication Department

  4. Example • Solve : x+5=0 Networks and Communication Department

  5. Quadratic equations Networks and Communication Department

  6. Example • Solve : Networks and Communication Department

  7. Plotting Symbolic Equations Networks and Communication Department

  8. Example 1: Networks and Communication Department

  9. Example 2: Networks and Communication Department

  10. Computing derivatives Networks and Communication Department

  11. Example • Find the derivative for : f = sin(5*x) Networks and Communication Department

  12. Integration Networks and Communication Department

  13. Example 1: • Find the integration for x^2 : Networks and Communication Department

  14. Example 2: Networks and Communication Department

  15. Convolution Networks and Communication Department

  16. 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. Networks and Communication Department

  17. Convolution Sum (Cont.) • The Figure below illustrates the definition of the impulse response h[n] and the relationship of Networks and Communication Department

  18. Example • Consider an LTI system with impulse response h[n] and input x[n]. Networks and Communication Department

  19. Networks and Communication Department

  20. x = [0.5 2 0 0 0]; h = [1 1 1 0]; y = conv(x,h); n1= 0 : (length(x)-1); subplot(2,2,1); stem(n1,x,’LineWidth’,3); xlabel(‘n’); ylabel(‘x[n]’); n2= 0 : (length(h)-1); subplot(2,2,2); stem(n2,h,’LineWidth’,3); xlabel(‘n’); ylabel(‘h[n]’); n3 = 0 : (length(y)-1); subplot(2,2,[3,4]); stem(n3,y,’LineWidth’,3); xlabel(‘n’); ylabel(‘y[n]’);

  21. The End Any Questions ? Networks and Communication Department

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