SIGNALS AND TRANSFORMS
Course Objectives:
1. To provide the basic understanding of signals and systems
2. To provide the knowledge of time- domain and frequency- domain representation of continuous-time & discrete-time periodic & a periodic signals

1. Signals and systems (7 hours)
1. Signal definition, continuous time signal, discrete time signal
2. Basic signal types: energy signal and power signal, periodic and aperiodic signal
3. Transformation of independent variable
4. Unit impulse and unit step functions
5. System definition, continuous time system, discrete time system
6. Basic system properties: system with and memory, invertibility, causality, stability, time invariance, linearity

2. Impulse Reponse and Convolution (6 hours)
1. Linear time invariant (LTI) systems and their properties
2. Continuous time LTI systems: Representation of continuous time signals in terms of impulses, Unit impulse response and convolution integral
3. Discrete time LTI systems: Representation of discrete time signals in terms of impulses, Unit impulse response and Convolution sum

3. Fourier Series (9 hours)
1. Fourier series representation of continuous time periodic signals
2. Properties of continuous time Fourier series (linearity, time shift, time reversal. Time scaling, multiplication, conjugation, convolution), Parseval’s relation
3. Fourier series representation of discrete time periodic signals
4. Properties of discrete time Fourier series, Parseval’s relation

4. Fourier Transforms (9 hours)
1. Fourier transform representation of continuous time aperiodic signal
2. 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
3. Discrete time Fourier transform, Properties of discrete time Fourier transform
4. Introduction to discrete time Fourier (DFT) and fast Fourier transform (FFT)

5. Sampling Theory (5 hours)
1. Representation of continuous time signal by its samples: Sampling
2. Spectral properties of sampled signal
3. Reconstruction of signal from its samples
4. Ideal sampling and practical considerations in sampling
5. Effect of under sampling: Aliasing

6. Z-transform and Difference Equations (9 hours)
1. Z-transform, convergence and region of convergence.
2. Properties of Z-transform (linearity, time shift, time reversal, multiplication by exponential sequence, differentiation, convolution, multiplication)
3. Z-Transform pairs
4. Inverse Z-transform by long division and partial fraction expansion
5. Discrete time systems described by difference equations
6. Solution of difference equations

Practical:

1. Signals and transform
2. Impulse Response and Convolution
3. Fourier Series
4. Fourier Transform
5. Sampling Theory
6. Z-transform and Difference Equations

Reference:

1. V. Oppenhiem, A.S. Willsky, S.H. Nawab, “Signals and Systems”, Prentice Hall
2. 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* 1,5.1-5.3 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.