Big FFT via Small-FFTs, Smoothing and Trend Leakage Reduction

Statistical requirements for many FFT spectrum-lines or time-samples often exceed computer memory for FFT processing in one large array. A solution is given for decomposing the large FFT, via "time-shuffling", into M smaller P-sample FFTs, where P = 2^Q samples. An example is given where a 65 K FFT was computed in 32 2-K FFT arrays by a small computer. The spectral variance was smoothed by a fast algorithm, a high-Q bandpass-filter magnitude-weighted averaging of 64 adjacent frequency points. The detection and subtraction of nonperiodic "trends" from the time-data, to reduce frequency "leakage" is also presented, via a useful sequential mechanization of the Moore-Penrose pseudo inverse, requiring only 360 bytes of array storage versus 2,359,296 bytes needed for its direct computation in the example given.