Spectral phase: from basics to video-rate application to tuning-fork resonance characterization

Abstract

Whereas graduated students are usually familiar with Fourier spectra, the spectral phase remains often mysterious to them. This paper proposes a “hands on.approach of discrete Fourier transform (DFT) and spectral phase. In a first part, basics of DFT are explored through elementary simulations. The variation of digital parameters allows the identification of sampled frequencies las well as their relation with the size of the sampled window. The significance of the spectrum phase is also illustrated experimentally to demonstrate the useful relationship between a displacement and the spectral phase. In a second part, these properties are put in application for the characterization of tuning-fork resonance by means of video-rate analysis of the spectral phase. Experimental hardware is reduced to elementary devices and remains affordable while involving all aspects of a measurement chain. The proposed progression constitutes a practical approach to discrete Fourier transform and spectral phase properties. At the end, the resonance curve of a tuning-fork is recorded in only a few minutes. The Shannon sampling theorem as well as the uncertainty relation linking the resolutions achieved in the direct and reciprocal domains, are also considered practically throughout this work.

Keywords

• fast fourier transform
• fourier phases
• tuning fork