Signals and Systems

The major aim of this course is to give an overall understanding of the fundamentals of signals and systems including various signal and system classifications, basic signal transformations, properties of linear systems, sampling and introducing various continuous and discrete Fourier representations of signals. These fundamentals form the foundation for understanding topics such as digital signal processing, control systems, digital image processing, computer vision and some key aspects of machine learning. Hence this course is required for students pursuing careers in the topics mentioned above.

The students shall be able to

• CO1: Classify both continuous and discrete-time signals and systems

• CO2: Differentiate between LTI and non-LTI systems and apply linear convolution operations to discrete and continuous systems

• CO3: Apply frequency analysis on periodic and non-periodic signals using Fourier series and transform techniques

• CO4: To demonstrate the understanding of sampling theory and apply signal analysis

• Introduction to Signals:

Introduction, Classification of Signals: Continuous time and discrete time, Even and odd, Periodic and non-periodic, Deterministic and random, Energy and Power Basic operations on signals: scaling, shifting, reflection, precedence rule for time shifting and time scaling. Elementary signals: Exponential, Sinusoidal, step, pulse, impulse, ramp, relationship between sinusoidal and complex exponential signals, Exponentially damped sinusoid signals

• Linear Systems and Convolution:

Convolution sum, Convolution integral, Interconnection of LTI systems, impulse response, step response, Relationship between impulse response and system properties, Properties of systems: Stability, Memory, Causality, Invertibility, Time invariance

• Laplace transforms:

Eigen Function property, Laplace transform representation, Convergence, S-place, Unilateral Laplace transform, ROC, properties.

• Fourier Series and Transforms (continuous ) :

Periodic signal-Fourier Series, Non Periodic signal-Fourier Transform, Properties of Fourier Representations, Parseval's Relationships, Duality property and its applications, Hilbert transform, Pre-envelope, Phase and Group delay.

• Fourier Representation of aperiodic discrete time signals

Periodic discrete signals, properties, Discrete time fourier transform, relation with the fourier series, properties.

• Sampling Theory:

Sampling continuous time signals, aliasing, Reconstruction-Ideal, practical

Texts:

1. Signals & Systems, 3^rd Ed., by Oppenheim, Wilsky and Nawab

(Alan V Oppenheim, Alan S Willsky, S Hamid Nawab, Signals and Systems, Pearson Education India; 2nd edition (1 January 2015))

2. Digital Signal Processing, Proakis

References:

1) Signals and Systems using Matlab (L Chaparro)

2) DSP using matlab (V. Ingle and J. Proakis)

3) Essential Matlab for Engineers and Scientists (B. Hahn, D. Valentine) 4) Signals and Systems by S. Haykin and Van Veen

5) H P Hsu, Schaums Outline Signals and systems, 2nd edition, McGraw Hill, 2008.

Homework & Quizzes: Analytical problems from the theoretical content

Computer assignments: Involves analysis and code development to solve a basic signals/systems problem

Lab Examination: lab examination

Theory Examinations: In-class examinations