The Discrete Fourier Transform, Part 6: Cross-Correlation.

Abstract

This paper is part 6 in a series of papers about the Discrete Fourier Transform (DFT) and the Inverse Discrete Fourier Transform (IDFT). The focus of this paper is on correlation. The correlation is performed in the time domain (slow correlation) and in the frequency domain using a Short-Time Fourier Transform (STFT). When the Fourier transform is an FFT, the correlation is said to be a "fast" correlation. The approach requires that each time segment be transformed into the frequency domain after it is windowed. Overlapping windows temporally isolate the signal by amplitude modulation with an apodizing function. The selection of overlap parameters is done on an ad-hoc basis, as is the apodizing function selection. This report is a part of project Fenestratus, from the skunk-works of DocJava, Inc. Fenestratus comes from the Latin and means, "to furnish with windows".