Signals, Transformations of Independent Variables, Basic Continuous Time Signals, Basic Discrete Time Signals, Systems, Properties of Systems, Linear Time - invariant Systems

Representation of Signals in terms of Impulses, Discrete Time LTI Systems, the Convolution Sum, Continuous Time LTI Systems, the Convolution Integral, Properties of LTI Systems, Systems Described by Differential and Difference Equations, Block Diagram Representation of LTI Systems Described by Differential Equations and, Singularity Functions, Analogy between Vectors and Signals, Orthogonal Vector and Signal Spaces, Approximation of a Function by a Set of Mutually Orthogonal Functions, Fourier Analysis of Continuous Time Signals and Systems, The Response of Continuous Time LTI Systems to Complex Exponentials, the Continuous Time Fourier series, Convergence of Fourier series, A-periodic Signals and Continuous Fourier Transform, Periodic Signals and Continuous Fourier Transform, Convolution and Modulation Property, Polar Representation of Continuous Fourier Transform, Frequency Response Characterized by Linear Constant Coefficient Differential Equations, First-order and Second-order Systems, Fourier Analysis of Discrete Time Signals and Systems Response of Discrete Time LTI Systems to Complex Exponential, Fourier Series, DTFT, Periodic Signals and DTFT, Properties of DTFT, Convolution, Modulation and Duality Property, Polar Representation of DTFT, First-order and Second-order Systems

Sampling Theorem, Reconstruction of a Signal from Samples, the Effect of Undersampling, Discrete Time Processing of Continuous Time Signals, Sampling in Frequency Domain, Sampling of Discrete Time Signals, Z-transform of a Discrete Sequence, Region of Convergence for the Z-transform, Inverse Z-transform, Properties of Z-transform, Relation Between Z and Fourier Transform