Numerical instability of deconvolution operation via block pulse functions

This paper characterizes oscillations found in block pulse function (BPF) domain identification of open loop first-order systems with step input. A useful condition for occurrence of such oscillations is presented mathematically. For any positive value of ‘ah’, oscillations are observed to occur, where h is the width of BPF domain sub-interval and 1 / a is the time constant of the first-order system under consideration.