On the detection and measurement of discontinuities

Studies the detection and size measurement of discontinuities from sampled noisy data of an univariate function. The proposed tests and estimators are of the form of linear convolution filters with characteristics employing series expansions. In particular, the standard and conjugate Fourier series are taken into consideration. The convergence properties (consistency and rate of convergence) of the proposed estimates are established. The asymptotic results model the performance of the estimates on grids which become increasingly fine, i.e., when the signal resolution increases. Unlike other techniques in the literature, no specific form of the underlying function is assumed, and behavior of the function in the neighborhood of the discontinuity need not be in the form of a step function