SIGNALS AND TRANSFORMS
Course Objectives:
 To provide the basic understanding of signals and systems
 To provide the knowledge of time domain and frequency domain representation of continuoustime & discretetime periodic & a periodic signals
 Signals and systems
(7 hours)
 Signal definition, continuous time signal, discrete time signal
 Basic signal types: energy signal and power signal, periodic and aperiodic signal
 Transformation of independent variable
 Unit impulse and unit step functions
 System definition, continuous time system, discrete time system
 Basic system properties: system with and memory, invertibility, causality, stability, time invariance, linearity
 Impulse Reponse and Convolution
(6 hours)
 Linear time invariant (LTI) systems and their properties
 Continuous time LTI systems: Representation of continuous time signals in terms of impulses, Unit impulse response and convolution integral
 Discrete time LTI systems: Representation of discrete time signals in terms of impulses, Unit impulse response and Convolution sum
 Fourier Series
(9 hours)
 Fourier series representation of continuous time periodic signals
 Properties of continuous time Fourier series (linearity, time shift, time reversal. Time scaling, multiplication, conjugation, convolution), Parseval’s relation
 Fourier series representation of discrete time periodic signals
 Properties of discrete time Fourier series, Parseval’s relation
 Fourier Transforms
(9 hours)
 Fourier transform representation of continuous time aperiodic signal
 Properties of continuous time Fourier tranform (linearity, time shift, time scaling, frequency scaling, conjugation, duality), Parseval’s relation, Energy spectral density and Power spectral density
 Discrete time Fourier transform, Properties of discrete time Fourier transform
 Introduction to discrete time Fourier (DFT) and fast Fourier transform (FFT)
 Sampling Theory
(5 hours)
 Representation of continuous time signal by its samples: Sampling
 Spectral properties of sampled signal
 Reconstruction of signal from its samples
 Ideal sampling and practical considerations in sampling
 Effect of under sampling: Aliasing
 Ztransform and Difference Equations
(9 hours)
 Ztransform, convergence and region of convergence.
 Properties of Ztransform (linearity, time shift, time reversal, multiplication by exponential sequence, differentiation, convolution, multiplication)
 ZTransform pairs
 Inverse Ztransform by long division and partial fraction expansion
 Discrete time systems described by difference equations
 Solution of difference equations
Practical:
 Signals and transform
 Impulse Response and Convolution
 Fourier Series
 Fourier Transform
 Sampling Theory
 Ztransform and Difference Equations
Reference:
 V. Oppenhiem, A.S. Willsky, S.H. Nawab, “Signals and Systems”, Prentice Hall
 G. Proakis, D.G. Manolakis, “Digital Signal Processing”, Prentice Hall
Assessments: Mean of three
Evaluation Scheme:
Marks distribution for all the chapters in the syllabus in shown in the table below.
Unit 
Hours 
Marks distribution* 
1,5.15.3 
7+2 
16 
2,5.4,5.6 
6+3 
16 
3 
9 
16 
4 
9 
16 
6 
9 
16 
Total 
45 
80 
*There may be minor variation in marks distribution.
