Testing for a Random Walk Structure in the Frequency Evolution of a Tone in Noise

Abstract

Inference and hypothesis testing are typically constructed on the basis that a specific model holds for the data. To determine the veracity of conclusions drawn from such data analyses, one must be able to identify the presence of the assumed structure within the data. In this paper, a model verification test is developed for the presence of a random walk-like structure in the variations in the frequency of complex-valued sinusoidal signals measured in additive Gaussian noise. This test evaluates the joint inference of the random walk hypothesis tests found in economics literature that seek random walk behaviours in time series data, with an additional test to account for how the random walk behaves in frequency space.

Time Variant Wave-Signal-Amplitude Trigonometry Regression of Latitudes and Longitudes of the Belmullets of the Atlantic Ocean

“…Affirmed by [30], among the problems usually encounter when dealing with oscillatory and wave signals are the decomposition of signals; periodicity transformation in generalization to timefrequency domain; and how to handle non-sinusoidal oscillatory signals. Among the developed algorithms to solve some of the mentioned problems are haemo-dynamic waveform analyses, accelerometer analysis for gait cadence, photoplethysmography (PPG), and detection of motion artifact in PPG.…”