Harmonic retrieval in nonstationary noise

Harmonic retrieval is a classical signal processing problem but it has been almost invariably assumed that the additive noise is stationary. In this paper, we abandon this requirement and allow the additive noise to be nonstationary (but also non-cyclostationary in order to distinguish it from the information bearing signal). We show that various FFT based approaches can still be used on a single record of data to yield frequency estimates that have the O(T^-3) variance, where T is the data length. Stationary multiplicative noise is also permitted in the model. Numerical examples illustrate the key concepts of the paper