# EC201

## Signals and Systems

Pre-Requisite: None
Contact Hours and Credits: (3 -0- 0) 3

### Objectives:

The aim of the course is for:

• Understanding the fundamental characteristics of signals and systems.
• Understanding the concepts of vector space, inner product space and orthogonal series.
• Understanding signals and systems in terms of both the time and transform domains, taking advantage of the complementary insights and tools that these different perspectives provide.
• Development of the mathematical skills to solve problems involving convolution, filtering, modulation and sampling.

### Topics Covered:

Vector spaces. Inner Product spaces. Schwartz inequality. Hilbert spaces. Orthogonal expansions. Bessel’s inequality and Parseval’s relations.

Continuous-time signals, classifications. Periodic signals. Fourier series representation. Hilbert transform and its properties.

Laplace transforms. Continuous - time systems: LTI system analysis using Laplace and Fourier transforms.

Sampling and reconstruction of band limited signals. Low pass and band pass sampling theorems. Aliasing. Anti-aliasing filter. Practical Sampling-aperture effect.

Discrete-time signals and systems. Z-transform and its properties. Analysis of LSI systems using Z - transform.

### Course Outcomes:

Students will be able to

• CO1: Apply the knowledge of linear algebra topics like vector space, basis, dimension, inner product, norm and orthogonal basis to signals.
• CO2: Analyse the spectral characteristics of continuous-time periodic and a periodic signals using Fourier analysis.
• CO3: Classify systems based on their properties and determine the response of LSI system using convolution.
• CO4: Analyze system properties based on impulse response and Fourier analysis.
• CO5: Apply the Laplace transform and Z- transform for analyze of continuous-time and discrete-time signals and systems.
• CO6: Understand the process of sampling and the effects of under sampling.

### Text Books:

A.V. Oppenheim et al, Signals and Systems (2/e), Pearson 200.

S.Haykin and B. VanVeen “Signals and Systems, Wiley, 1998.

M. Mandal and A. Asif, “Continuous and Discrete Time Signals and Systems, Cambridge, 2007.

### Reference Books:

D.C. Lay, Linear Algebra and its Applications (2/e), Pearson, 200.

K. Huffman & R. Kunz, Linear Algebra, Prentice- Hall, 1971.

S.S. Soliman & M.D. Srinath, Continuous and Discrete Signals and Systems, Prentice- Hall, 1990.