EE 257 Signals and Systems

Content

1.0 Introduction

1.1 Classification of Signals

Continuous and Descrete time signals
Continuos and Descrete valued signals
Deterministic and Random Signals
Energy and Power signals
Odd and Even signals Periodic and Aperiodic Signals

1.2 Special Signals

Complex Exponential Signals
Impulse
Unit Step

1.3 Continuous and Descerete time Systems

1.3.1 Inter Connections Between Systems

    Cascaded
    Parallel
    Series - Parallel Feedback

1.3.2 System Properties

    System with or without memory
    Inverse Systems
    Time Invariance Linearity *Causility

1.4 Operations On signals

Time Delay
Time Scaling
Negation

1.5 Linear Time Invarient Systems

1.5.1 Convolution For Descrete LTI system

1.5.2 Convolution For Continous LTI system

1.6 Properties of Convolution

Commutativity Distributivity *Condition for Inverse
Laplace Transform of Convolution

2.0 Fourier Series

2.1 Introduction

2.1.1 Inter-domain Analysis

2.1.2 Periodic Signals

2.1.3 Vector Space

2.2 Fourier Series

2.2.1 Introduction

2.2.2 Coefficients of Fourier Series

2.3 Properties of Fourier Series

2.3.1 Linearity

2.3.2 Time shifting

2.3.3 Time Reverse

2.3.4 Time Scaling

2.3.5 Properties For Real Signals

    Real and Even
    Real and Odd

2.3.6 Differentiation and Integration

2.3.7 Fourier Series of an Impulse

2.4 Trignometric Fourier Series

2.5 Power of a periodic signal

Parseval's Theorem

2.6 Periodic Signal through LTI system

3.0 Fourier Transform

3.1 Introduction

3.1.1 Complex Valued Functions

3.1.2 From F.S. to F.T.

3.1.3 Fouries Transform and Inverse F.T.

3.1.4 F.T. and L.T.

3.2 Fouries Transforms of Signals

3.2.1 
 and 

3.2.2 Delta Function 

3.2.3 Square Pulse

3.2.4 Unit Step Function 

3.3 Properties of F.T.

3.3.1 Linearity

3.3.2 Time Shifting

3.3.3 Modulation / Shifting in Frequency

3.3.4 Differentiation and Integratino

3.3.5 Time Scaling

3.3.6 Time Reversal

3.3.7 Uses of Properties (examples of derivations)

F.T. of Periodic Signals

3.4 F.T. properties of real signals

Real signals
Real even signals
Real Odd signals

3.5 Duality

3.6 Energy of the signal

Parseval's Theorem

3.6 Modulation

3.7 L.T.I. systems and F.T.

3.7.1 Frequency response

3.7.2 Convolution Property

3.7.3 Differentiation Property