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A new procedure is presented for calculating the complex, discrete Fourier transform of real-valued time series. This procedure is described for an example where the number of points in the series is an integral power of two. This algorithm preserves the order and symmetry of the Cooley-Tukey fast Fourier transform algorithm while effecting the two-to-one… (More)
After describing, applying, comparing, and evaluating four major methodologies, this guided tour concludes with an interim procedure for use until the "right" method appears.
1. Introduction. Cooley and Tukey stated in their original paper  that the Fast Fourier Transform algorithm is formally most efficient when the number of samples in a record can be expressed as a power of 3 (i.e., N = 3m), and further that there is little efficiency lost by using N = 2m or N = 4™. Later, however, it was recognized that the symmetries of… (More)
This tutorial considers the structure and construction of reliable software. By way of introduction, several of the structured programming and software engineering techniques are classified into three groups; those which impact primarily on the program structure, the development process, and the development support tools. Structural Analysis Concepts are… (More)
We describe why these papers were chosen, and categorize them in terms of major contribution, underlying model of the software life-cycle, and applicability to various types of system.