**Signals and Systems**

### OBJECTIVES:

The main objectives of this course square measure given below:

â€¢ To introduce the word of signals and systems.

â€¢ To introduce Fourier tools through the analogy between vectors and signals.

â€¢ To introduce the construct of sampling and reconstruction of signals.

â€¢ to research the linear systems in time and frequency domains.

â€¢ to check z-transform as mathematical tool to research discrete-time signals and systems.

#### UNIT- I:

INTRODUCTION: Definition of Signals and Systems, Classification of Signals, Classification of Systems, Operations on signals: time-shifting, time-scaling, amplitude-shifting, amplitude-scaling. issues on classification and characteristics of Signals and Systems. complicated exponential and curved signals, Singularity performs and connected functions: impulse function, step perform signum perform and ramp perform. Analogy between vectors and signals, orthogonal signal area, Signal approximation mistreatment orthogonal functions, Mean sq. error, closed or complete set of orthogonal functions, Orthogonality in complicated functions.

#### UNIT â€“II:

Fourier series AND FOURIER TRANSFORM: Fourier series illustration of continuous time periodic signals, properties of Fourier series, Dirichletâ€™s conditions, pure mathematics Fourier series and Exponential Fourier series, complicated Fourier spectrum. derivation Fourier remodel from Fourier series, Fourier remodel of discretional signal, Fourier remodel of ordinary signals, Fourier remodel of periodic signals, properties of Fourier transforms, Fourier transforms involving impulse perform and Signum perform. Introduction to David Hilbert remodel.

#### UNIT â€“III:

SAMPLING THEOREM â€“ Graphical and analytical proof for Band restricted Signals, impulse sampling, Natural and Flat high Sampling, Reconstruction of signal from its samples, impact of beneath sampling â€“ Aliasing, Introduction to Band Pass sampling.

#### UNIT-IV:

ANALYSIS OF LINEAR SYSTEMS: Linear system, impulse response, Response of a linear system, Linear time invariant (LTI) system, Linear time variant (LTV) system, construct of convolution in time domain and frequency domain, Graphical illustration of convolution, Transfer perform of a LTI system. Filter characteristics of linear systems. Distortion less transmission through a system, Signal information measure, system information measure, Ideal LPF, HPF and BPF characteristics, relation and Poly-Wiener criterion for physical realization, relationship between information measure and rise time.

Cross-correlation and auto-correlation of functions, properties of correlation perform, Energy density spectrum, Parsevalâ€™s theorem, Power density spectrum, Relation between machine correlation perform and energy/power spectral density perform. Relation between convolution and correlation, Detection of periodic signals within the presence of noise by correlation, Extraction of signal from noise by filtering.

#### UNIT â€“V:

mathematician|Pierre Simon de Laplace|mathematician|astronomer|uranologist|stargazer} TRANSFORMS : Review of Laplace transforms, Partial fraction growth, Inverse astronomer remodel, construct of region of convergence (ROC) for astronomer transforms, constraints on mythical monster for varied categories of signals, Properties of L.Tâ€™s, Relation between L.Tâ€™s, and F.T. of a symbol. astronomer remodel of sure signals mistreatment wave synthesis.

II Year – I Semester

L T P C

4 0 0 3 ** SIGNALS & SYSTEMS **

#### UNIT â€“VI:

Zâ€“TRANSFORMS : basic distinction between continuous-time and discrete-time signals, separate signaling illustration mistreatment complicated exponential and curved parts, cyclicity of separate time mistreatment complicated exponential signal, construct of Z- remodel of a separate sequence. Distinction between astronomer, Fourier and Z transforms. Region of convergence in Z-Transform, constraints on mythical monster for varied categories of signals, Inverse Z-transform, properties of Z-transforms.

#### TEXT BOOKS:

- Signals, Systems & Communications – B.P. Lathi, BS Publications, 2003.
- 2. Signals and Systems – A.V. Oppenheim, A.S. Willsky and S.H. Nawab, PHI, 2nd Edn.
- 3. Signals & Systems- Narayan Iyer and K Satya Prasad, Cenage Pub.

#### REFERENCE BOOKS:

- Signals & Systems – Simon Haykin and Van Veen, Wiley, 2d Edition. 2. Principles of Linear Systems and Signals â€“ BP lathee, university Press, 2015 3. Signals and Systems â€“ K Raja Rajeswari, B VisweswaraRao, PHI, 2009 4. Fundamentals of Signals and Systems- Michel J. Robert, MGH International Edition, 2008. 5. Signals and Systems â€“ T K Rawat , university press, 2011

#### OUTCOMES:

At the top of this course the scholar can in a position to:

â€¢ Characterize the signals and systems and principles of vector areas, construct of orthgonality.

â€¢ Analyze the continuous-time signals and continuous-time systems mistreatment Fourier series, Fourier remodel and astronomer remodel.

â€¢ Apply sampling theorem to convert continuous-time signals to discrete-time signal and reconstruct back.

â€¢ perceive the relationships among the varied representations of LTI systems

â€¢ perceive the ideas of convolution, correlation, Energy and Power density spectrum and their relationships.

â€¢ Apply z-transform to research discrete-time signals and systems.