Guest editorial [On digital frequency analysis for audio engineers]

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Abstract
One of the last places one might look for a discussion of digital frequency analysis would be in the IEEE Transactions on Audio and Electroacoustics. A paper by Cooley and Tukey (1965) described a recipe for computing Fourier coefficients of a time series that used many fewer machine operations than did the straightforward procedure. This saving in computation can amount to a factor of as much as several hundred for usefully long stretches of data. Almost simultaneously G. Sande at Princeton University developed another algorithm of the same class. He used it to calculate covariances with equally impressive saving, though not of the same magnitude. Procedures that provide reductions in complexity of this order may rightfully be called breakthroughs. After the publication of Cooley and Tukey's paper a number of earlier papers were discovered describing the essentials of the fast Fourier transform. But, as has happened often in other fields, these papers appeared too early, and solved a problem whose importance had not yet been adequately recognized. Besides making digital spectrum analysis more attractive from an economic standpoint, the fast Fourier transform (FFT) has changed the concepts of digital filtering, in that the intellectually appealing approach of filtering in the frequency domain is now very often simpler and quicker than by convolution, even though two transforms between time and frequency are employed. In the use of digital systems, the important barrier between the time- and frequency-domains has been significantly lowered. Given the on-going intensive and widespread development in digital circuit technology, this means that many new applications for digital processing will be opened up. The audio engineer who naturally thinks only in terms of analog processing might well become familiar with what the digital approach is now able to offer. He may be surprised. What lies over the horizon in digital processing is anyone's guess, but I think it will surprise us all.

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