Detection of signal discontinuities from noisy fourier data

The concentration method for identifying the locations, magnitudes, and signs of jump discontinuities in analog signals from truncated Fourier series is well established in mathematical literature. Its performance in the presence of noise on the Fourier data has only recently started to receive attention, however. This paper examines the performance of the concentration method in the presence of noise from a detection-theoretic point of view. In particular, receiver operating characteristics for the elemental problem of detecting a unit step discontinuity are developed for this method. Additionally, the problem of optimally combining data obtained from multiple concentration factors is addressed.