Computationally efficient updating of a weighted Welch periodogram for nonstationary signals

In this paper we introduce a computationally efficient method for updating a weighted Welch periodogram for nonstationary signals. Non-parametric spectral estimation techniques, such as the Welch periodogram, are highly mature topics in signal processing. They have a wide variety of applications in signal analysis including real-time applications with modern test and measurement systems. In many of these real-time applications the data is nonstationary having a power spectrum that is changing over time. This paper introduces a method of generating a weighted update of the Welch periodogram as more data becomes available. We find that for a certain class of weighting functions a computationally efficient algorithm can be found. The paper also presents calculations of the computational complexity of the updating algorithm and simulations for nonstationary signals.