Fourier analysis with Lissajous figures

Abstract

A practical method for Fourier analysis of a periodic waveform using only low-cost equipment is described. The method is suitable for any periodic voltage signal whose frequency can be continuously varied. By employing multistage tuning it can realize an accuracy that is limited only by that of the waveform of the test signal. The method is didactic and has the aesthetic appeal of the myriad variations of Lissajous figures. It is also suitable for mass duplication as a standard classroom experiment in the undergraduate laboratory. Exemplary results are shown for the square and triangular waves generated with simple circuit designs.

Lissajous-like figures with triangular and square waves

“…One may argue, on such basis, that it is a straightforward mathematical procedure to outguess the Lissajous-like figures reported here and computer simulations are needless. Although one can use Lissajous figures to Fourier analyze a given signal [17] the other way around (use Fourier analysis to forecast Lissajous-like figures) is not as easy. To see this let us expand, for instance, the square wave in Fourier series.…”

Some applications of Fourier's great discovery for beginners

“…where m < 1 is called the modulation index. Equation (5) shows that the AM generates new frequencies, ωand ω+ , called sidebands. The sidebands are symmetrically located around the high frequency, often called the carrier.…”

“…For those, the period is accepted to be infinity, and the summation is replaced by integration. Fourier analysis constitutes an important part of laboratory courses [2][3][4][5][6][7][8][9][10][11][12][13]. Higgins [2] presented an introduction to this technique.…”

“…Higgins [2] presented an introduction to this technique. It is very natural to use an LC resonant circuit for separating the harmonics [3][4][5]. Sandoval and Porta [6] presented an analysis of the vibration of a string using optical detection.…”

Investigating properties of white noise in the undergraduate laboratory

“…For example, this concept has already been elegantly introduced in [1]. The concept of the Fourier transform is also extensively explored in laboratory experiments in areas as diverse as optics, quantum mechanics and signal processing [1][2][3][4]. The present paper describes an experiment which simultaneously investigates various properties of electrical noise and its frequency composition.…”