Statistical Properties of a Modified Welch Method That Uses Sample Percentiles

TL;DR

This paper introduces a robust spectral estimation method using sample percentiles instead of averaging, providing analytical bias and variance expressions validated with Gaussian noise data.

Contribution

It proposes a novel spectral estimator based on sample percentiles, enhancing robustness over traditional Welch's method.

Findings

Bias and variance formulas match empirical data

Method performs well with white Gaussian noise

Provides a more robust spectral estimation approach

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.