16EC403

**UNIT I****INTRODUCTION TO SIGNALS AND SYSTEMS: **Classification of signals – Periodic

and Aperiodic, Energy and Power, Deterministic and Random, Complex exponential and

Sinusoidal signals. Basic Signals, Operations on signals. Systems: Definition and

Classification.**FOURIER SERIES REPRESENTATION OF PERIODIC SIGNALS:** Representation of

Fourier series, Continuous time periodic signals, properties of Fourier series, Dirichlet‘s

conditions, Trigonometric Fourier series and Exponential Fourier series, Complex Fourier

spectrum. Discrete Time Fourier Series-Properties.

**UNIT II****FOURIER TRANSFORMS:** Deriving Fourier Transform from Fourier series, Fourier

transform of arbitrary signal, Fourier transform of standard signals, Fourier transform of

periodic signals, properties of Fourier transforms. Discrete Time Fourier TransformProperties.

**UNIT III****SIGNAL TRANSMISSION THROUGH LINEAR SYSTEMS:** Linear system, impulse

response, Response of a linear system, linear time-invariant (LTI) system, linear time variant

(LTV) system, Transfer function of a LTI system. Filter characteristics of linear systems.

Distortion less transmission through a system, Signal bandwidth, system bandwidth, Ideal

LPF, HPF and BPF characteristics.**SAMPLING:** Sampling theorem – Graphical and analytical proof for Band Limited Signals,

impulse sampling, Natural and Flat top Sampling, Reconstruction of signal from its samples,

Effect of under sampling – Aliasing, Introduction to Band Pass sampling.

**UNIT IV****CONVOLUTION AND CORRELATION OF SIGNALS: **Concept of convolution in time

domain and Frequency domain, Graphical representation of convolution, Convolution

property of Fourier transforms. Cross correlation and auto correlation of functions, properties

of correlation function, Energy density spectrum, Parseval‘s theorem, Power density

spectrum, Relation between auto correlation function and energy/power spectral density

function, Relation between convolution and correlation, Detection of periodic signals in the

presence of noise by correlation, Extraction of signal from noise by filtering.

**UNIT V****LAPLACE TRANSFORMS:** Review of Laplace transforms (L.T), Partial fraction

expansion, Inverse Laplace transform, Concept of region of convergence (ROC) for Laplace

transforms, Constraints on ROC for various classes of signals, Properties of L.T, relation

between L.T, and F.T. of a signal. Laplace transform of certain signals using waveform

synthesis.

Z–TRANSFORMS: Fundamental difference between continuous and discrete time signals,

discrete time signal representation using complex exponential and sinusoidal components,

Periodicity of discrete time signals, Concept of z-transform of a discrete sequence,

Distinction between Laplace, Fourier and z-transforms, Region of convergence in ztransform,

constraints on ROC for various classes of signals, Inverse z-transform, properties

of z-transforms.

**TEXT BOOKS:**

1. Signals, Systems & Communications – B.P. Lathi, 2009,BS Publications.

2. Signals and Systems – A.V. Oppenheim, A.S. Willsky and S.H. Nawab, PHI, 2nd Edn.

**REFERENCES:**

1. Signals and Systems – A. Ramakrishna Rao – 2008, TMH.

2. Linear Systems and Signals – B. P. Lathi, Second Edition, Oxford University press, 2008.

3. Fundamentals of Signals and Systems Michel J. Robert, MGH International Edition, 2008.

4. Signals, Systems and Transforms – C. L. Philips, J. M. Parr and Eve A. Riskin, Pearson

education.3rd Edition

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