Basic discrete-time signals. Discrete-time LTI systems. Representation of discrete-time signals in terms of impulses. The convolution sum. Properties of discrete-time LTI systems: memory, invertibility, causality and stability. The discrete-time Fourier transform. Frequency response of systems characterized by difference equations.
The z-transform: definition, properties and region of convergence for the z-transform. Relationship of the z-transform to the discrete-time Fourier transform. Analysis of LTI systems characterized by difference equations. Stability and causality in discrete-time LTI systems. The inverse z-transform.