A calculator for numerical Fourier synthesis

The customary numerical method of Fourier synthesis, using three figure tables, is accurate but laborious and slow. The calculator described makes the method ten times faster, and the accuracy is about the same. It is especially useful for the occasional synthesis which does not justify an automatic machine. For each of twelve harmonics, expressed in the form Rk sin (k + kθ), numerical values are obtained for θ = 0°, 7½°, 15°,... 352½°. These are recorded on a work-sheet and the sum k = 12 Σ Rk sin (k + kθ) is got by simple addition for each value of θ. Full use is made of the k = 1 frequent recurrence of values for some harmonics in order to minimize the number of readings that must be taken from the calculator. The principle is applicable to any values of k and any of the commonly used intervals of θ. A mechanical Fourier synthesizer of simple construction for handling fifteen harmonics is described in an appendix. This instrument enables the synthesized waveform to be plotted directly.