Signals And Systems. Representation of SignalsContinuous and discrete time signals: Classification of signals - periodic aperiodic even - odd - energy and power signals - deterministic and random signals - complex exponential and sinusoidal signals - periodicity - properties of discrete time complex exponential unit impulse - unit step impulse functions - transformation in independent variable of signals: time scaling, time shifting. Determination of Fourier series representation of continuous time and discrete time periodic signals - explanation of properties of continuous time and discrete time Fourier series. Analysis of Continuous Time Signals and SystemsContinuous time Fourier transform and Laplace transform analysis with examples - properties of the continuous time Fourier transform and Laplace transform basic properties, Parseval s relation, and convolution in time and frequency domains.
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Signals And Systems. Signal AnalysisAnalogy between vectors and signals, Orthogonal signal space, Signal approximation using orthogonal functions, Mean square error, Closed or complete set of orthogonal functions, Orthogonality in complex functions, Exponential and sinusoidal signals, Concepts of Impulse function, Unit step function, Signum function.
Fourier TransformsDeriving Fourier transform from Fourier series, Fourier transform of arbitrary signal, Fourier transform of standard signals, Fourier transform of periodic signals, Properties of Fourier transforms, Fourier transforms involving impulse function and Signum function. Introduction to Hilbert transform. Filter characteristics of linear systems. Convolution and Correlation of SignalsConcept of convolution in time domain and frequency domain, Graphical representation of convolution, Convolution property of Fourier transforms.
Relation between convolution and correlation, Detection of periodic signals in the presence of noise by correlation, Extraction of signal from noise by filtering. SamplingSampling 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.
T's relation between L. T's and F. T of a signal. Laplace transform of certain signals using waveform synthesis. Distinction between Laplace, Fourier and z-Transforms. Region of convergence in z-transform, Constraints on ROC for various classes of signals, Inverse z-transform, Properties of z-transforms.
Chapter3 Fourier Transform 31 to Laplace Transforms 7 1to7. Chapter 8 zTransfbrms 81 to 8. Chapter 5 Convolution and Correlation of Signals o Signals And Systems Dr. Signals And Systems J. Signals and Systems J.
Signals & Systems
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Signals And Systems. Definitions of a signal and a system, Classification of signals, Basic operations on signals, Elementary signals, Systems viewed as interconnections of operations, Properties of systems. Time-domain representations for LTI systems-1 : Convolution, Impulse response representation, Convolution sum and convolution integral. Time-domain representations for LTI systems- 2 : Properties of impulse response representation, Differential and difference equation representations, Block diagram representations.