Informatica

The discrete Fourier transform (DFT) is used for determining the coefficients of a transfer function for n‐order singular linear systems, Ex⁽ⁿ⁾=Σi=1ⁿAix⁽ⁿ⁻¹⁾+Bu, where E may be singular. The algorithm is straight forward and easily can be implemented. Three step‐by‐step examples illustrating the application of the algorithm are presented.

This paper contains measures to describe the matrix impulse response sensitivity of state space multivariable systems with respect to parameter perturbations. The parameter sensitivity is defined as an integral measure of the matrix impulse response with respect to the coefficients. A state space approach is used to find a realization of impulse response that minimizes a sensitivity measure.

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.