Syllabus Signals and Systems - (BE04009051) Total Credits = TH / 30 Assessment Pattern and Marks Total Marks Theory Tutorial / Practical ESE (E) PA (M) PA (I) PBL (I) ESE (V) 4 70 30 20 30 50 200 Unit No. Content 1 Introduction to Signals : Introduction to Continuous-Time(CT) and Discrete-Time(DT) Signals, Size of a Signal (CT & DT), Signal Energy and Power (CT & DT), Classification of Signals (CT & DT), Elementary signals (CT & DT), (Unit step function, Unit impulse function Exponential, Discrete-Time Sinusoid, Discrete-Time Complex Exponential) and their properties, Basic Operations on Signals (CT & DT) (Time Shifting, Time Scaling, Time Reversal, Addition, Subtraction, Multiplication), Even and Odd functions, Application in electrical engineering (e.g. Representation of input current waveform of 12 pulse rectifier as addition of periodic square and pulse signals). (Chapter - 1) 2 Introduction to Systems : Definition and representation of CT and DT systems, Classification of system (CT & DT) (Linear and Nonlinear Systems, Time-Invariant and Time-Varying Systems, Instantaneous and Dynamic Systems, Causal and Non-causal Systems, Invertible and Non-invertible Systems, Stable and Unstable Systems), Application of concepts learned in electrical engineering (e.g. Importance of linearity and time invariance in analysis of any electrical system, Linearization of a non-linear system about an operating point to analyse it as a linear system). (Chapter - 2) 3 Time-Domain Analysis of CT and DT Systems : The Unit Impulse Response of CT and DT Linear Time-Invariant(LTI) Systems, Impulse response characterization of CT and DT LTI systems, The convolution sum and integral, Properties of convolution sum and integral, Application of convolution integrating in obtaining the response of series RL and RC circuit. (Chapter - 3) 4 Fourier analysis of CT and DT signals : Periodic CT and DT Signal Representation by Trigonometric and Exponential Fourier Series, Fourier Spectra of a periodic CT and DT signal for trigonometrical and exponential Fourier series representation, Dirichlet’s Conditions, Effect of wave symmetry on Fourier series coefficients, Properties of CT and DT Fourier series, Parseval’s Theorem, CT and DT aperiodic signal representation by the Fourier Transform, Fourier Spectra of an periodic CT and DT signal, Properties of CT and DT Fourier Transform, Application of Fourier analysis in Electrical engineering (e.g. Fourier analysis of inverter output voltage and current to design a filter, Fourier analysis of utility voltage and current waveforms during fault to take protective action). (Chapter - 4) 5 CT System Analysis using Laplace Transform and DT System Analysis using z-Transform : Introduction to the Laplace Transform, Finding the Inverse Transform, Properties of Laplace Transform, Connection Between the Fourier and Laplace Transforms, Properties of Laplace Transform, Solution of Differential and Integro-Differential Equations, Introduction to the z-Transform, Inverse Transform by Partial Fraction Expansion and Tables, Inverse z-Transform by Power Series Expansion, Connection Between the DTFT and the z-Transform, Transforms, Properties of z-Transform, Solution of Linear Difference Equations using z-Transform. (Chapter - 5) 6 Sampling and Reconstruction : Representation of a Continuous-Time Signal by Its Samples, The Sampling Theorem, Impulse-Train Sampling, Sampling with a Zero-Order Hold, Reconstruction of a Signal from Its Samples Using Interpolation, The Effect of Under sampling : Aliasing. (Chapter - 6)
