Low peak factor waveforms for efficient system analysis using a fast Fourier transform

Abstract

Low peak factor waveforms [M. R. Schroeder, Number Theory in Science and Communication (Springer, New York, 1984)] can be designed so that multiple harmonics in the waveform appear to have the ideal spectrum of a true Fourier transform when the waveform is analyzed using a fast Fourier transform (FFT). If the harmonics in the waveform are restricted to those having an integral number of cycles in the FFT data record length, there is no leakage, and the magnitudes and phases of the Fourier coefficients are identical to those of the harmonics in the waveform. Low peak factor waveforms drastically reduce peak power requirements. For example, the peak power requirement for a waveform having 63 harmonics can be reduced by a factor of about 30. Waveforms can be designed having harmonics with constant, octave, and close approximations to one‐third octave frequency differences. This approach can provide an efficient alternative to other methods in current use for measuring system transfer functions. [Work supported in part by the National Research Council of Canada and the Lanikai Foundation.]