Causal Systems & Transforms: Delay Operator Interpretation

This lecture discusses the concept of z Variable as a Delay Operator in the context of LTI causal systems and transforms. It covers the interpretation of z-1 as a delay operator, the implementation of realizable systems, and the distinction between FIR and IIR systems. The lecture also explores random variables, cumulative distribution functions, moments, and correlation in the context of probability theory. Additionally, it delves into the properties of discrete time stochastic processes, including stationarity, correlation, covariance, and power spectral density. The lecture concludes with an overview of Hilbert Spaces, explaining the inner product, norm, and projection theorem.