## SIGNALS & 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 idea 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. advanced exponential and curving signals, Singularity operates and connected functions: impulse function, step operate signum operate and ramp operate. Analogy between vectors and signals, orthogonal signal house, Signal approximation exploitation orthogonal functions, Mean sq. error, closed or complete set of orthogonal functions, Orthogonality in advanced functions.

### UNIT â€“II: series AND FOURIER TRANSFORM:

series illustration of continuous time periodic signals, properties of series, Dirichletâ€™s conditions, pure mathematics series and Exponential series, advanced Fourier spectrum. explanation Fourier remodel from series, Fourier remodel of impulsive signal, Fourier remodel of normal signals, Fourier remodel of periodic signals, properties of Fourier transforms, Fourier transforms involving impulse operate and Signum operate. Introduction to David Hilbert remodel.

### UNIT â€“III: SAMPLING THEOREM â€“

Graphical and analytical proof for Band restricted Signals, impulse sampling, Natural and Flat prime 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, idea of convolution in time domain and frequency domain, Graphical illustration of convolution, Transfer operate 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 operate, Energy density spectrum, Parsevalâ€™s theorem, Power density spectrum, Relation between motor vehicle correlation operate and energy/power spectral density operate. 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:

Pierre Simon de Laplace|Pierre Simon de Laplace|mathematician|astronomer|uranologist|stargazer} TRANSFORMS : Review of Laplace transforms, Partial fraction enlargement, Inverse Marquis de Laplace remodel, idea of region of convergence (ROC) for Marquis de Laplace 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 proof. Marquis de Laplace remodel of bound signals exploitation wave shape synthesis.

### UNIT â€“VI:

Zâ€“TRANSFORMS : basic distinction between continuous-time and discrete-time signals, distinct signaling illustration exploitation advanced exponential and curving elements, regularity of distinct time exploitation advanced exponential signal, idea of Z- remodel of a distinct sequence. Distinction between Marquis de Laplace, 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, Bachelor of Science 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, Cengage Pub.

### REFERENCE BOOKS:

- Signals & Systems – Simon Haykin and Van Veen, Wiley, second Edition. 2. Principles of Linear Systems and Signals â€“ BP club, Oxford 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 , Oxford 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, idea of orthgonality.

â€¢ Analyze the continuous-time signals and continuous-time systems exploitation series, Fourier remodel and Marquis de Laplace remodel.

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

â€¢ perceive the relationships among the assorted 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.