Computer Fourier-transform techniques for precise spectrum measurements of oscillatory data with application to the de Haas–van Alphen effect

Abstract

Methods are developed for the high-accuracy analysis of oscillatory data using the discrete fast Fourier transform. A wide dynamic range and linearity of response together with good separation of individual lines in a spectrum are achieved by using digital filtering to reduce the sidelobes to less than −120 dB relative to the central peak. Periodic errors associated with the discrete nature of the transform are reduced by interpolation fitting. To make use of the high accuracy inherent in the digital data, a least-squares method is developed which fits line shapes accurately matched to the digital filter to the Fourier-transform spectrum. Frequencies are measured to an accuracy (computational) of better than 0.00001% and amplitudes to better than 0.001%. Although more generally applicable to problems requiring highly precise spectral analysis, the techniques are here directed to the analysis of de Haas–van Alphen oscillations where many frequencies are present and amplitudes are a strong function of magnetic field. An interpretation is made of the ’’amplitude’’ from which it is possible to calculate frequencies (i.e., Fermi surface areas), Dingle temperatures (i.e., electron scattering times), and effective masses with an accuracy (computational) of 0.00005% or better. This accuracy is realized for a discrete record having only a modest number of data points.