Feasible LID Systems: Transfer Functions and Stability

This lecture covers the concept of feasible LID systems, which are characterized by being implementable using a finite number of memory registers. It explains how feasible LID systems are governed by rational transfer functions and the importance of poles being inside the unit circle for stability. The lecture also delves into the implications of causality and stability in achievable time systems, emphasizing the necessity of the unit circle containment. Additionally, it explores the implementation parameters, complexity of calculations, and the historical perspective on the cost of operations in computing. The presentation concludes with discussions on direct and recursive implementations of filters, trellis implementation, and the significance of reflection coefficients in speech processing.