This chapter explores some adaptive filtering topics which are important to applied adaptive signal processing technology. The implications for national defense and security were obvious and scientists and engineers throughout the world began to focus on new adaptive algorithms for reducing noise and estimating kinematic states such as position, velocity, acceleration, and so on. Pole–zero filters, also known as autoregressive moving average Auto Regressive Moving Average (ARMA) filters, pose special convergence problems which must be carefully handled in the adaptive filters which whiten ARMA signals, or attempt to identify ARMA systems. The chapter presents frequency domain adaptive processing with the Least-mean Square (LMS) algorithm. Performance limitations due to slow LMS algorithm convergence are the main reason for high interest in fast adaptive algorithms. The frequency domain LMS algorithm is also of great interest for applications where the error and/or other signals are best expressed in the frequency domain.