Continuous Time Signal And Systems
SignalsElementary Continuous Time (Ct) signals like unit step, impulse, ramp, exponential, sinusoidal etc. Operations on signal like shifting, flipping, scaling, addition, multiplication. Breaking of a CT signal in different basic componentsSystemsConcept of system modeling, Classification of system on the basis of linearity, time variance, causality, memory etc. System representation by a differential equation, System response in terms of Linear convolution integral.The Fourier SeriesOrthogonal basis functions, Representation of a signal in terms of weighed Orthogonal basis functions, Calculation of weights (coefficients) in MSE sense, Extension to periodic signal in terms of Fourier series representation, Complex and trigonometric Fourier series, Properties of Fourier series, Power Specral Density.The Fourier Transform (FT)Definition and properties, FT of basic signals, FT of periodic signals, Energy Specral Density.Laplace TransformReview of single sided Laplace transform, its properties and methods of Inverse Laplace transform, Two sided Laplace transform, Concept of region of convergence, Relationship between Laplace and Fourier transformTime Domain Behavior of a SystemApplication of a Laplcace transform to a system differential equation, Transfer function and its properties for a linear, lumped & stable systems, Impulse response of a system, Zero input and zero state response of a system, Time domain analysis for a first and second order systems, Condition for BIBO stability in time domain, System response to complex exponential inputs.Frequency Domain Behavior of a SystemPole-zero diagram, Frequency response of a system by analytical and graphical techniques, Stability and Routh Array, Bode plotAnalog to Digital Conversion & ReconstructionSampling theorem and Aliasing, Anti aliasing filter, ReconstructionState-Variable TechniquesState-Variable concepts. State equations and their time domain and frequency domain solutions, State transition matrix, System state equations.