## 1 Introduction  
The recent complete sequencing of genomes [1-3] has led to an urgent need for new methods for genomic data analysis. At most 5% of the human genome codes for proteins: the function of most of the remaining 'junk' DNA is unknown [4]. Fourier transform methods have frequently been used in the analysis of DNA sequences, particularly in the identification of coding regions [5-7]. The degeneracy of the genetic code results in the likely repeat of T nucleotides in every third position: this gives a peak at 3 in the power spectrum of an exotic sequence. Several workers have used Fourier techniques to detect a sequence periodicity of between 10 and 11 bp [8,9] in genomic sequences, related to the DNA helical repeat. The results are sufficiently sensitive to distinguish between periodicities of 10 bp in archebacteria and 11 bp in eubacteria [8]. [PERSON] has observed a periodicity of 10.2 bp in the occurrence of AA dinucleotides in eukaryotic but not prokaryotic genomes [10]. This is probably related to the related to the preferential positioning of nucleosomes in eukaryotes. Fourier techniques have also been used in the alignment of nucleosomal DNA sequences [11] and in the prediction of nucleosome array formation [12]. Very recently, Fourier methods have been used in two new contexts. [PERSON] _et al_ have reported a Fourier transform method, SWIFT, for identifying protein sequences of a given class from the raw DNA sequence [13]. [PERSON] _et al_ have developed the Spectral Repeat Finder to look for the location of both tandem and dispersed repeats [14]. Their method is somewhat similar to the method we propose for DNA structural properties. Spectral Repeat Finder uses the power spectrum of a DNA sequence to find the length of any repetitive element, followed by a windowing technique to locate the precise DNA repeat. Recently we have applied Fourier transform techniques in an analysis of the structural properties of sets of Ultra Conserved Elements (UCEs) [15], and Conserved Non-Genic sequences (CNGs) [16,17]. Each of these sets contain sequences which are highly conserved between mouse and human over hundreds of bases. We showed that the power spectra of certain structural properties were able to distinguish coding from non-coding elements and also that a subset of the UCEs contained a repeating 6.2 bp 3-step roll motif [18]. In previous work we constructed the potential energy surfaces for all octamers in double helical DNA, as a function of the two principal degrees of freedom, slide and shift at the central step [19-24]. Analysis of these potential energy maps allowed us to compile a database of the structural properties of all 32, 896 unique DNA octamers, including information on stability, the minimum energy conformation and flexibility [25,26]. In a very recent analysis of methylated versus non-methylated CpG islands, certain of these structural properties, in particular high rise and low twist were found to be highly correlated with CpG island methylation and were used in the very successful prediction of further methylation patterns [27]. The structural properties considered here are summarised in Table 1. One concept may be unfamiliar. The ability of a DNA sequence to adopt a specific overall shape depends on the ability of dinucleotide steps to adapt their structure to fit the conformational preferences of their neighbours. Structural variation at the dinucleotide level may be compensated for by conformation changes in the neighbouring dinucleotides. This has the effect of smoothing variation along the sequence. We therefore defined a new set of 3-step parameters that allow for the smoothing effect of two neighbouring steps on the properties of the central step. To obtain these parameters for an octamer, we consider the outer base pairs of the central three base steps (four base pairs) and calculate the overall values of roll, twist, slide and shift as if this was one giant base step [26]. The properties may be considered as belonging to one of two classes.