Module I:
Signals and systems as seen in everyday life, and in various branches of engineering and science. Energy and power signals, continuous and discrete time signals, continuous and discrete amplitude signals.

System properties: linearity: additivity and homogeneity, shift-invariance, causality, stability, realizability.

Module II:

Linear shift-invariant (LSI) systems, impulse response and step response, convolution, input-output behaviour with aperiodic convergent inputs. Characterization of causality and stability of linear shift invariant systems. System representation through differential equations.
Module III:
Periodic and semi-periodic inputs to an LSI system, the notion of a frequency response and its relation to the impulse response, Fourier series representation, the Fourier Transform, convolution/multiplication and their effect in the frequency domain, magnitude and phase response, Fourier domain duality. The Discrete-Time Fourier Transform (DTFT) and the Discrete Fourier Transform (DFT). Parseval’s Theorem. The idea of signal space and orthogonal bases.

Module IV:
Evolution of Transforms: Fourier Transform, Laplace Transform , Z-transform (single sided and Double sided) The Laplace Transform, notion of eigen functions of LSI systems, a basis of eigen functions, region of convergence, poles and zeros of system, , solution to differential equations and system behaviour using Laplace Transformation The z-Transform for discrete time signals and systems- eigen functions, region of convergence, z-domain analysis.

Module V:
The Sampling Theorem and its implications- Spectra of sampled signals. Reconstruction: ideal interpolator, zero-order hold, first-order hold, and so on. Aliasing and its effects. Relation between continuous and discrete time systems.