Signals and Systems using SCILAB

Analog Systems
Chapter 1.: Signals and their Representations
a. Definition of a Signal
b. Periodic Continuous Time Signals
c. Discrete Time Signals
d. Non periodic Signals
e. Representing signals by Orthogonal Functions
f. Orthogonal Polynomials
g. Power Signals and Energy Signals
h. Interpolating signals by use of Polynomials
Chapter 2.: Continuous Time Systems
a. Properties of continuous time Systems
b. Convolution
c. The Impulse Response of the system
d. Operators of the System
Chapter 3.: Spectrum of Periodic Signals
a. The Fourier Series
b. Effects of Symmetry
c. Parseval's Theorem
d. The Generalized Fourier Series
Chapter 4.:Spectrum of Time Domain Signals
a. The Fourier Transform
b. Characteristic of Linear Systems
c. Other types of Transforms. The Hilbert Transform
Chapter 5.: The Laplace Transform
a. The Bilateral and the one sided Laplace Transform
b. The Inverse Laplace Transform
c. Properties of the Laplace Transform
d. Transfer function of the LTI System
e. Signal Flow Graph representation of the LTI System
f. The Inverse Laplace Transform
g. Using Laplace Transform to solve differential Equations with initial conditions
h. The Bode plot
Chapter 6.: Continuous Time State Space Systems
a. State Equations for linear systems
b. Solutions to Continuous time State Equations
c. Properties of the Fundamental Matrix
d. Laplace Transform Solution to the State Equations
e. Initial State Vectors and the Initial Conditions
f. Observing the state of the system. Observers and Observability
g. Controlling the state of the system. Controllers and Controllability
h. Liapunov Stability Criteria

Digital Systems
Chapter 7.: Discrete Signals and Systems
a. The Linear Difference Equation
b. Solution of the First Order Linear Difference Equation
c. The Delay Operator and the Discrete time system
d. Discrete Time Convolution Summation
e. Frequency Response of Discrete time systems
f. Sampling a continuous time signal
g.