Online frequency band estimation and change-point detection

Detecting change-points in time series is at the heart of numerous applications, as abrupt changes in signal properties are quite common in natural and industrial processes. In this paper we propose an algorithm for a particular change-point detection problem where the frequency band of the signal changes at some points in the time axis. Apart from detecting the change-points, the proposed algorithm is also able to estimate the frequency bands. The main idea of the algorithm is to consider a simple local bandlimited model to represent the input signal in each sliding time window. The local model consists of a sum of two exponentials that, in the frequency domain, reads as the transfer function of a second order bandpass filter. Relying on the operational calculus, we obtain an explicit estimation of the parameters, that indicate the cut-off frequencies associated to each time window. The implementation is done in discrete time domain where the cut-off frequencies are computed as a combination of outputs of several FIR filters, providing a low computational cost online estimation. Experimental results show the efficiency and the stability of this algorithm even in presence of a moderate amount of noise.