Statistical Properties of a Modified Welch Method That Uses Sample Percentiles

Abstract

We present and analyze an alternative, more robust approach to the Welch's overlapped segment averaging (WOSA) spectral estimator. Our method computes sample percentiles instead of averaging over multiple periodograms to estimate power spectral densities (PSDs). Bias and variance of the proposed estimator are derived for varying sample sizes and arbitrary percentiles. We have found excellent agreement between our expressions and data sampled from a white Gaussian noise process.