A Procedure for Implementing the Fast Fourier Transform on Small Computers

A technique has been developed that adapts the Fast Fourier Transform algorithm for implementation on computers having relatively long multiplication times. The technique is particularly well suited to real-time processing on a small data acquisition computer such as the IBM System/7. Four basic ideas are utilized to improve the performance of the original Cooley-Tukey algorithm on such a machine: 1) The real-valued nature of the input data is exploited. 2) The number of multiplications that must be carried out is minimized at the expense of additions. 3) The calculations are performed in a carefully ordered sequence. 4) Special multiplication algorithms are used. This technique has reduced by more than an order of magnitude the time required to carry out 1024-point transformations on a small computer. A program is developed for calculating these transforms in real time on an IBM System/7 computer. With this program, a maximum sampling rate in excess of 10 kHz is obtained.