Course : Signals and Systems
Course code : 4709
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Objectives of signal processing, Classification of signals based on time and amplitude, Characteristic signal parameters, Classification of signals based on Energy and Power, Transformations of the independent variable, Categories of continuous-time signals.
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10/12/26 | ||
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Unit step function, Impulse function (Delta function), Signal representation using the Delta function, Unit ramp, Exponential signals (real and complex), Sinusoidal signals, Pulses (rectangular and triangular), Sampling function, Impulse train (Comb signal).
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10/12/26 | ||
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Definition and categories of systems (Continuous-time systems, Discrete-time systems), System interconnections, Types of systems (Linear and non-linear systems, Causal and non-causal systems, Static and dynamic systems, Time-invariant and time-varying systems, Stable and unstable systems).
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10/12/26 | ||
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Description of Linear Time-Invariant (LTI) systems (via ordinary differential equations, via the convolution integral), Impulse response of LTI systems, The convolution integral in LTI systems, Properties of convolution (Commutative property, Associative property, Distributive property, Identity property, Homogeneity property, Scaling property).
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10/12/26 | ||
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Analytical computation of the convolution integral, Graphical method for computing the convolution integral, Convolutions of known continuous-time signals, System step response, System response to a complex exponential input, Interconnections of LTI systems.
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10/12/26 | ||
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Eigenvalues of an LTI system, Mathematical definition of the Laplace transform, Region of convergence of the Laplace transform, Poles and zeros of the Laplace transform, Useful Laplace transform pairs.
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10/12/26 | ||
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Properties of the Laplace transform, Symmetries of the Laplace transform, Time-domain and frequency-domain convolution theorems, Initial and final value theorems, Calculation of the inverse Laplace transform (Partial fraction expansion method, Heaviside method, Terms with exponential delay).
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10/12/26 | ||
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Review of eigenfunctions, Conditions for the existence of a Fourier series, Signal expansion into a Fourier series (Exponential form, Trigonometric form I, Trigonometric form II), Normalized power of the Fourier expansion, Parseval's theorem for periodic functions, Gibbs phenomenon, Relationship between Fourier series and Fourier transform.
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10/12/26 | ||
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Definition of the Fourier transform, Physical significance of the Fourier transform, Conditions for the existence of the Fourier transform, Relationship between Fourier and Laplace transforms, Properties of the Fourier transform, Parseval's theorem, Useful Fourier transform pairs.
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10/12/26 | ||
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Inverse Fourier Transform, Fourier Transform of Power Signals, Correlations and Spectral Densities, Autocorrelation Function, Cross-correlation Function.
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10/12/26 | ||
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Solving Linear Differential Equations using the Laplace Transform, System Transfer Function, Stability and Causality Analysis in the Frequency Domain, System Interconnections in the Frequency Domain, Step Response of an LTI System, State-Space System Description.
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10/12/26 | ||
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Frequency Response of an LTI System, Magnitude and Phase Representation of Frequency Response, Response of an LTI System to Periodic Input, Response of an LTI System to Non-Periodic Input, Description of Linear Differential Equations via Fourier Transform, Inverse Systems.
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10/12/26 | ||
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Ideal Linear Frequency-Selective Filters (Ideal Low-Pass Filter, Ideal High-Pass Filter, Ideal Band-Pass Filter, Ideal Band-Stop Filter), Characteristic properties of ideal filters, Filter bandwidth, Practical filters, Standard low-pass analog filters.
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10/12/26 |