Signals & Systems II: Filter Implementations

This lecture covers the direct and recursive implementations of IIR filters, focusing on the 'numerator-denominator' and 'denominator-numerator' forms. It discusses the benefits of canonical implementation, reduced storage, and minimum delays. The lecture also explores trellis implementation, stability, and the transfer function of causal and stable systems. Additionally, it delves into the discrete-time Fourier transform (DTFT), its properties, and its link with the Z-transform, emphasizing the periodicity and convergence aspects. The lecture concludes with an analogy between eigenvectors and Fourier analysis in LID systems.