Demystifying DFT-Based Harmonic Phase Estimation, Transformation, and Synthesis

• Type: Other Publications
• Date: 2024

Authors

Oliveira, M (Author) Other; Santos, V (Author) Other; Saraiva, A (Author) Other; Aníbal Ferreira (Author) FEUP

Other information

Authenticus ID: P-017-JWA

DOI: 10.20944/preprints202409.0098.v1

Abstract (EN): <jats:p>Many natural signals exhibit a quasi-periodic behavior and are conveniently modeled as a combination of several harmonic sinusoids whose relative frequencies, magnitudes and phases vary with time. The waveform shape of those signals reflects important physical phenomena underlying their generation, which requires that those parameters be accurately estimated and modeled. In the literature, accurate phase estimation and modeling has received much less research effort than frequency estimation, or magnitude estimation. First, this paper addresses accurate DFT-based phase estimation of individual sinusoids in six scenarios involving two DFT-based filter banks and three different windows. It is shown that bias in phase estimation is less than 1E-3 radians when the SNR is equal to or larger than 2.5 dB. Taking as a reference the Cramér-Rao Lower Bound, it is shown that one particular window offers a performance of practical interest by approximating better the CRLB when signal conditions are favorable, and by minimizing the performance deviation when signal conditions are adverse. Second, this paper explains how a shift-invariant phase-related feature can be devised that characterizes harmonic phase structure, which motivates a signal processing paradigm that greatly simplifies parametric modeling, transformation and synthesis of harmonics signals, in addition to facilitating the understanding and reverse engineering of the phasegram. Theory and results are discussed in a reproducible perspective using dedicated experiments that are supported with code allowing not only to replicate figures and results in this paper, but also to expand research.</jats:p>

Language: English

Type (Professor's evaluation): Scientific