Application of Mathematics in Signals & Systems

IE 211   

APPLICATIONS  OF MATHEMATICS IN SIGNALS AND SYSTEMS

 

Teaching Scheme

   

Examination Scheme

Lectures : 3 hrs/week

 

Mid-Sem – 30, Assignments, Quiz -20

 

 

End-Sem Exam- 50.

 

Unit 1 

   

(06)

Statistical Analysis of signals                                                                 

Mean, Medium, and mode, standard deviation, variance, moments, coefficient of skew ness & kurtosis, correlation & line of regression

 

Unit 2 

   

(06)

Probability                                                                                                  
Theorems on Probability, Conditional Probability, Baye’s theorem, Probability density functions (binomial, Poisson, normal) distribution function, standard deviation, chi-square test, probable error and combination of system component errors, overall system accuracy calculations, overall error from root mean square formula

 

Unit 3 

   

(06)

Introduction to Signals and Systems:                                                           

Introduction to Signals, Classification of Signals, Continuous Time and Discrete Time Signals, Step and Impulse Functions, Transformation of Independent Variable. Introduction to Systems, Classification of Systems, Properties of Systems, Normal Form of System Equation, Initial Conditions, Impulse Response of a Physical System, Introduction to Convolution, System Impulse Response.

 

Unit 4 

   

(06)

Analysis of Systems                                                                                   
System characteristics, Convolution Sum, Sampling theorem, reconstruction, aliasing, sampling in the frequency domain, sampling of discrete time signals, decimation and interpolation. Properties and applications of Z transform

 

 

 

 

Unit 5 

   

(08)

Fourier Transform Analysis                                                                   
Fourier analysis for Continuous time signals and systems, Continuous time Fourier series and its convergence, Continuous time Fourier Transform, its properties, frequency response. 

 

Unit 6 

   

(08)

Discrete Fourier Transform

Discrete time Fourier series and its convergence, Discrete time Fourier Transform, its properties, frequency response. Introduction to DFT in time domain and frequency domain.

Filtering: Ideal frequency selective filters, Non Ideal frequency selective filters, examples, Butterworth filters.

 

Text Books

·         Signals and Systems By Michael J. Robert, TMH, New Delhi, Edition 2003

·         Probability and Statistics, Spiegel, Schiller and Srinivasn, Second Edition, Scaum’s Outline TMH

 

Reference books

 
·        Signals and systems, Oppenheium, Willsky Pearson (low price) second edition

 

 

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