Learn Signals and Systems (Signal Processing) from Scratch

Some useful operations on signals: Time shifting, Time scaling, Time inversion. Signal models: Impulse function, Unit step function, Exponential function, Even and odd signals. Systems: Linear and Non-linear systems, Constant parameter and time varying parameter systems, Static and dynamic systems, Causal and Non-causal systems, Lumped Parameter and distributed parameter systems, Continuous-time and discretetime systems, Analog and digital systems.

Fourier series: Signals and Vectors, Signal Comparison: correlation, Signal representation by orthogonal signal set, Trigonometric Fourier Series, Exponential Fourier Series, LTI system response to periodic inputs.

Continuous-Time Signal Analysis:  Fourier Transform of arbitrary signal, standard signals, periodic signals, Fourier Transforms involving Impulse function and Signum function, Properties of Fourier Transform, Introduction to Hilbert Transform, Signal transmission through LTI Systems, ideal and practical filters, Signal energy. Laplace transform: Definition, some properties of Laplace transform, solution of differential equations using Laplace transform, Inverse Laplace Transform, Partial fraction expansion method for inverse LT, Relation between LT and Fourier Transform.

Concept of convolution in Time domain and Frequency domain, Graphical representation of Convolution, Cross Correlation and Auto Correlation of functions, Relation between Convolution and Correlation. Properties of Correlation function, Parseval’s Theorem. Relation between Auto Correlation function and Energy/Power spectral density function, Detection of periodic signals in the presence of Noise by Correlation, Extraction of signal from noise by filtering.

Sampling 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.