Fourier transform of delta compressed data

Abstract

Delta compression is a well-known, simple and efficient method for compressing smooth data sequences by using differences between successive values, instead of the values themselves. This kind of data sequence results after digitalization of physical signals in many scientific, medical, industrial, and other applications. Many of them use discrete Fourier transform (DFT) as a part of the data treatment. In this work, the Fourier transform directly over delta-compressed data is investigated. It is shown that the Fourier coefficients of the original data can be calculated in a simple manner from the Fourier coefficients of the compressed data sequence without decompression. DFT on delta-compressed data using delta-compressed pre-computed basis functions (sine and cosine) values is also considered. It is shown that this greatly reduces required memory space and computational time. Possible applications of these results are discussed.