FFT window functions - Chris Bore

Fordwater, Pond Road, Woking, Surrey GU22 0 JZTelephone: (01483) 740138 Fax: (0148) 740136 email: Web: window functionsFFT window functions Limits on FFT analysisLimits on FFT analysisWhen using FFT anaysis to study thefrequency spectrum of signals, thereare limits on resolution betweendifferent frequencies, and ondetectability of a small signal in thepresence of a large are two basic problems: thefact that we can only measure thesignal for a limited time; and thefact that the FFT only calculatesresults for certain discrete frequencyvalues (the 'FFT bins'). The limit onmeasurement time is fundamentalto any frequency analysis technqiue:the frequency sampling is peculiarto numerical methods like the measurement timeLimited measurement timeThe first problem arises because thesignal can only be measured for alimited time. Nothing can be knownabout the signal's behaviour outsidethe measured interval. We have toassume something about the signaloutside the measured interval, andthe Fourier Transform makes animplicit assumption that the signal isrepetitive: that is, the signal withinthe measured time repeats for real signals will havediscontinuities at the ends of themeasured time, and when the FFTassumes the signal repeats it willassume discontinuities that are notreally sharp discontinuities havebroad frequency spectra, these willcause the signal's fr

Fordwater, Pond Road, Woking, Surrey GU22 0JZ Telephone: (01483) 740138 Fax: (0148) 740136 email: bores@bores.com Web: http://www.bores.com FFT window functions

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