The document provides an overview of signal analysis in MATLAB, focusing on polynomials and their manipulation in Scilab. It discusses the creation, determinants, and derivatives of polynomials, as well as solutions to linear equations represented as matrix equations. Additionally, it covers definite integration in Scilab, demonstrating the evaluation of definite integrals using various functions.

1. Signal Analysis in MATLAB
BY, MR. DIGAMBAR PURI
Polynomial in SCILAB

2. Overview
• Polynomials
• Determinants of Polynomials
• Derivatives in SCILAB
• Solution to Linear Equations
• Definite Integration

3. Polynomials in SCILAB

4. Polynomials
• Examples:

5. Polynomials
• A polynomial can be
expressed directly after
declaring variable

6. Polynomials
• Examples in SCILAB
• 1] 3]
• 2] 4]

7. Polynomials
• A polynomial can be created in two ways. One way is to define the
polynomial in terms of its roots and the other way is to define it in
terms of its coefficients.

8. Polynomials

9. Other commands in Polynomial

10. Polynomial Arithmetic

11. Polynomial Matrix
• A polynomial can be
expressed in matrix form

12. Determinants of
Polynomials in SCILAB

13. Determinants of Matrix
•

14. Determinants of Polynomial Matrix
•

15. Derivatives of
Polynomials in SCILAB

16. Derivatives of Polynomial Matrix
• A polynomial can be expressed in matrix form

17. Plotting of Polynomials

18. Polynomial Plotting

19. Polynomial Plotting

20. Solutions of Linear
Equations in SCILAB

21. Linear Equations
• A system of n linear equations and m variables is given by,

22. Linear Equations
• This system of Linear equations can be written as Matrix
Equations,
• If we define the following Matrices as,

23. Linear Equations
• Case 1: A system with same number of equations and unknowns:
Unique Solution Exists
• Example:

24. Linear Equations

25. Linear Equations
• The null space returned for A is empty, indicating unique solution

26. Linear Equations
• Exercise Problems
1) 2)
3) 4)

27. Linear Equations
• Case 2: A system with same number of equations and unknowns:
No unique Solution Exists
• Example:

28. Linear Equations
•
• The first two rows are same indicate same parallel lines (det=0)

29. Linear Equations
• Case 3: A system with more number of unknowns than equations:
More than one Solution Exists
• Example:
• We can write a matrix equation.

30. Linear Equations
• By Appling the function linsolve to this system,

31. Linear Equations
• Case 4: A system with more equations than unknowns:
No results

32. Linear Equations
•

33. Magic Square
• The function test matrix can also produce matrices corresponding
to magic squares.
• Matrices such that sum of rows and columns, as well as it’s
diagonals, produce the same results.

34. Definite Integration
in SCILAB

35. Definite Integration
evaluates the definite integral from a to b of f(t)dt. The
function f(t) should be continuous.
Y= integrate(‘sin(x)’,’x’,0,2);
Y= integrate(‘x*x,’x’,0,1);

36. Some basic functions
in SCILAB

37. Basic Functions

38. Thank You...