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1.1 Signal Analysis & Fourier Series : Analogy between vectors and signals-Orthogonal signal space-Signal approximation using orthogonal functions-Mean square error
1.2 Closed or complete set of orthogonal functions-Orthogonality in complex functions-Exponential and sinusoidal signals-Concepts of Impulse function
1.3 Unit step function-Signum function-Representation of Fourier series-Continuous time periodic signals, Properties of Fourier series
1.4 Dirichlet’s conditions-Trigonometric Fourier series and Exponential Fourier series-Complex Fourier spectrum
2.1 Fourier Transforms & Sampling: Deriving Fourier transform from Fourier series-Fourier transform of arbitrary signal-Fourier transform of standard signals
2.2 Fourier transform of periodic signals-Properties of Fourier transforms-Fourier transforms involving impulse function and Signum function
2.3 Introduction to Hilbert Transform- Sampling theorem -Graphical and analytical proof for Band Limited Signals-Impulse sampling
2.4 Natural and Flat top Sampling-Reconstruction of signal from its samples-Effect of under sampling – Aliasing- Introduction to Band Pass sampling
3.1 Signal Transmission Through Linear Systems : Linear system-Impulse response-Response of a linear system-Linear time invariant (LTI) system
3.2 Linear time variant (LTV) system-Transfer function of a LTI system - Filter characteristics of linear systems-Distortion less transmission through a system
3.3 Signal bandwidth-System bandwidth-Ideal LPF, HPF and BPF characteristics
3.4 Causality and Paley-Wiener criterion for physical realization-Relationship between bandwidth and rise time
4.1 Convolution And Correlation Of Signals : Concept of convolution in time domain and frequency domain- Graphical representation of convolution-Convolution property of Fourier transforms
4.2 Cross correlation and auto correlation of functions-Properties of correlation function- Energy density spectrum-Parseval’s theorem-Power density spectrum
4.3 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
5.1 Laplace Transforms :Review of Laplace transforms- Partial fraction expansion- Inverse Laplace transform
5.2 Concept of region of convergence (ROC) for Laplace transforms-Constraints on ROC for various classes of signals-Properties of L.T’s, Relation between L.T’s, and F.T. of a signal
5.3 Laplace transform of certain signals using waveform synthesis
6.1 Z–Transforms: Fundamental difference between continuous and discrete time signals-Discrete time signal representation using complex exponential and sinusoidal components-Periodicity of discrete time using complex exponential signal-Concept of Z- Transform of a discrete sequence
6.2 Distinction between Laplace, Fourier and Z transforms-Region of convergence in Z-Transform, Constraints on ROC for various classes of signals
6.3 Inverse Z-transform - Properties of Z-transforms
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CategoriesElectronics & Communication
Format EPUB
TypeeBook