Informatica

Statistical properties are examined for a class of pipelined-block linear time-varying (LTV) and linear time-invariant (LTI) discrete-time systems. Pipelined-block equations are derived, using the general solution of LTV discrete-time system in state space. Afterwards, we analysed the state covariance and output covariance matrices of pipelined-block LTV and LTI discrete-time systems in state space. For this class of pipelined-block realizations expressions are found for calculation of characteristics of the roundoff noise. Finally, scaling in the pipelined LTV discrete-time systems in state space is considered.

For pipelining and block processing in linear time-varying (LTV), linear periodically time-varying (LPTV), and linear time-invariant (LTI) discrete-time systems, we suggest to use the general solution of state space equations. First, we develop three pipelined-block models for LTV, LPTV, and LTI discrete-time systems, and two pipelined-block structures. Afterwards, we analyse complete state controllability, complete output controllability, and complete observability of LTV and LTI pipelined-block discrete-time systems.

In this paper, we propose to present the direct form recursive digital filter as a state space filter. Then, we apply a look-ahead technique and derive a pipelined equation for block output computation. In addition, we study the stability and multiplication complexity of the proposed pipelined-block implementation and compare with complexities of other methods. An algorithm is derived for the iterative computation of pipelined-block matrices.