Adaptive tests for periodic signal detection with applications to laser vibrometry
Initially motivated by a practical issue in target detection laser vibrometry, we are interested in the problem of periodic signal detection in a Gaussian fixed design regression framework. Assuming that the signal belongs to some periodic Sobolev ball and that the variance of the noise is known, we first consider the problem from a minimax point of view: we evaluate the so-called which corresponds to the minimal distance between the signal and zero so that the detection is possible...