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.

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.

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.