||Elementary Signals, Classification and representation of continuous time and discrete time signals, Signal operations. Continuous time and discrete time systems – Classification, Properties. Representation of systems: Differential equation representation of continuous time systems. Difference equation representation of discrete systems. Continuous time LTI systems and convolution integral. Discrete time LTI systems and linear convolution. Stability and causality of LTI systems. Correlation between signals, Orthogonality of signals.
||Frequency domain representation of continuous time signals – continuous time Fourier series and its properties. Continuous time Fourier transform and its properties. Convergence and Gibbs phenomenon
Review of Laplace Transform, ROC of Transfer function, Properties of ROC, Stability and causality conditions. Relation between Fourier and Laplace transforms.
||Analysis of LTI systems using Laplace and Fourier transforms. Concept of transfer function, Frequency response, Magnitude and phase response.
Sampling of continuous time signals, Sampling theorem for lowpass signals, aliasing.
||Frequency domain representation of discrete time signals, Discrete time fourier series for discrete periodic signals. Properties of DTFS. Discrete time fourier transform (DTFT) and its properties.
Analysis of discrete time LTI systems using DTFT. Magnitude and phase response.
||Z transform, ROC, Inverse transform, properties, Unilateral Z transform.
Relation between DTFT and Z-Transform, Analysis of discrete time LTI systems using Z transforms. Transfer function. Stability and causality using Z transform.