signalsandsystems

Brief Introduction to the Course

This course will introduce you to concepts of signals and systems as applied to the domain of electrical and electronics engineering. In this domain, a signal is function in the form of voltage or current depending on one or more independent variables namely time or space; while system is often a circuit or a machine that processes the signals often into a desired form.

More general idea of a signal being a representation of some information/knowledge and the system as any 'transformation', 'black box' or a 'set up' that will transform its `input signal' to an 'output signal' (in most cases of different characteristics than the input) is certainly helpful. This approach has helped in creating many 'useful' technological aids, has solved numeral technical problems and provided many innovations; besides helping in understanding the physical world around us.

Course Structure

Entire course will be of the duration of total seventy hours running for appriximately 14 weeks (5 hrs /week); out of which 40 hours will be class lecture and remaining hours will be spent on tutorial. A week's course consists of three hours of lecture and two hours of tutorial. Tutorial hours will be utilized for problem solving, simulation and MATLAB exercises. Surprise quizzes may also be given during the tutorial hour.

Science/Engineering package MATLAB will be extensively used as a part of the course. Students are also encouraged to learn other open source packages such as SCILAB or OCTAVE.

Grading Policy:

Continuous Internal Evaluation (CIE) - 50%

Semester End Examination - 50%

Continuous Internal Evaluation (CIE) comprises of

3 Internal Tests of 25 Marks Each. . (Event #1,3,5)

Quizes - 10 Marks . (Event #2)

Case study and Presentation - 15 Marks . (Event #4)

Total CIE - 100 Marks

Syllabus

Unit 1

Introduction: Signals in continuous and discrete time, Transformation of independent variable, Exponential and sinusoidal signals, Unit impulse and unit step functions, Continuous and discrete-time systems, System properties: with/without memory, invertibility and inverse systems, linearity, causality, time invariance/variance, stability.

Linear Time Invariant Systems: Convolution Integral, Convolution sum, Linear Constant Coefficient Differential Equations, Linear Constant Coefficient Difference Equations, Commutative, Distributive, Associative Property, Invertibility, Causality, Stability, Block diagram representation and analysis.

(Ch1, Ch 2.1 to Ch 2.4) (8 hours)

Unit 2

Fourier series representation of periodic signals in continuous time; Properties, Fourier series representation of periodic signals in discrete time, Properties, Fourier series and LTI systems, Filtering. Simple RC high pass, low pass filter. Continuous Time Fourier transform: Properties, Examples of analog filters, Magnitude and phase representation of FT, Magnitude-Phase representation of frequency response of LTI, Analysis of first order and second order LTI systems using CFT.

(Ch 3, 4, 6.1, 6.2, 6.5) (8 hours)

Unit 3

Discrete Time Fourier transform: Properties, Duality, Examples of digital filters, Analysis of first order and second order LTI systems using DFT, Sampling Theorem and Reconstruction, Effect of under-sampling; aliasing, Communication systems: AM with complex exponential and sinusoid as carrier, Demodulation for sinusoidal AM, Frequency Division Multiplexing, PAM, Discrete time modulation.

(Ch 5, 6.6, 7.1, 7.2, 7.3, 8.1, 8.2, 8.3, 8.6, 8.8) (8 hours)

Unit 4

Introduction, Laplace transform, region of convergence, inverse Laplace transform, Relation with Fourier transform of continuous time signals, Properties of LT, Some standard pairs, Analysis of continuous LTI systems using LT, System interconnection and LT, Unilateral LT,

Introduction to Z-transforms, region of convergence, inverse Z-transform, relation with FT of discrete time signals, Properties of ZT, some standard pairs, Analysis of discrete time LTI systems using ZT, System interconnection and ZT, Unilateral ZT, Recursive (IIR) and nonrecusive (FIR) filters.

(Ch 9, 10) (8 hours)

Unit 5

Introduction to Linear Feedback Systems, Some applications and consequences of feedback, Rootlocus analysis, PID control, State-space model, state transition matrix, state-variable feedback, Linear time varying systems, state transition matrix for LTV systems, Systems over Boolean field, finite state machine, examples.

(Ch 11) (8 hours)

Text Book & References

TEXT BOOK:

1. Signals and Systems by Oppenheim, Wilsky, Hamid, Prentice-Hall Engineering/Science/Mathematics (Pearson Education Low price Indian edition also available), 2001.

References:

1. Signals and Systems, Nagarath, Sharan, Rakesh, Ranjan, Tata McGraw Hill, Special Indian Edition, 2000

2. Control Systems Engineering, Norman Nise, John-Wiley and sons, 3^rd edition, 2001.

3. An Introduction to Analog and Digital Communications, Simon Haykin, John-Wiley & Sons, 1999.

4. Digital Signal Processing, Oppenheim and Schafer, Pearson Education, special Indian edition, 2000.

5. Digital Signal Processing: Principles, Algorithms and Applications, 4th Edition, Proakis, Manolakis, Prentice Hall India, 2007.

6. Switching and Finite Automata Theory, Kohavi, Tata-McGraw Hill, 2^nd edition.

Related Links

1. MATHWORKS creators of MATLAB
2. SCILAB free open source package similar to MATLAB
3. IEEE