Fourier Analysis Using A Spreadsheet

F or many tasks involving Fourier analysis, a spreadsheet is an excellent tool. Using examples, this article shows that for data sets involving perhaps a hundred points and a few tens of coefficients, a spreadshe& method is practical and quick on perwnal computers such as the Macintosh SE or the IBM PC AT and compatibles. With enhanced hardware such as floating-point co-pmcaasor chips, the numbers may be extended by about an order of magnitude. This article presents three spreadsheet templates that should permit, rather easy generalization to other onhogonal bask functions, provided those can be defined in t e r n of standard functions or recurrence formulas. Fourier analysis is used here to illustrate pmvision of modularity to spreadsheet element definitions, so that the available replication processes allow simple extension of the ranges of the calculation; in this case, the number of harmonics and integration nodes. Fourier analysis of a real function also illustrates some techniques in spreadsheet use. These include selective application of array/vector arithmetic and the important trick of formulating formula blocks that can be replicated (blocks copied with relative referances adjusted appropriately and absolute references unchanged) to extend the range or resolution of the calculation. For a moderate problem, programming and debugging of functional Fourier analysis templates like the Fourier templates discussed below might take a spreadsheet user less time than finding the user's manual and the object code for an existing Fourier analysis pmgram. The reader is assumed to have some experience with Excel or a similar spreadsheet program so the general operations given here can be carried out without detailed instructions. The examples use the R l a option for addressing the elements of the template; thii is a matter of taste, but has the pmperty that variable names can take the form a0 and b1, which othewise conflict with the slightly mom compact normal addressing scheme All AB137, ... . ' h w templates for the Exoel spreadsheet pmgram illustrate the trade-off between extensive use of memory for possible reduction of calculation time and, amversely, the deliberate recalculation of data to mduce memory quirements. Fast Fourier transform (FiT) techniques am not used here because the logic required is not straightforwardly well suited to the simpler tools available in the spreadsheet. By development of function macms for migrade indexing, formula entry and logic, the FET or the related