On recursive discrete Fourier transformation

It is shown that the recent deadbeat state-observer approach to discrete Fourier transform evaluation is exactly equivalent to the nonrecursive frequency-sampling filters of finite impulse response digital filter design. The approach is then extended to consider the Kalman filter derived from the signal model and this is demonstrated to be nonrobust and pathological. The application of state observers to this problem is then brought into question and it is shown that they have a novel application to signal processing between the extremes of deadbeat and Kalman observers.