Language Reference

FFT

Trace Windows The FFT algorithm assumes the source trace array is one period of an in￿nitely long string of concatenated, duplicate arrays. Thus, the beginning

and end elements of the source trace array must gradually diminish to zero amplitude. If the end points of the original trace array are of di￿erent magnitude, the resulting array series could contain discontinuities that introduce high wavelength components into the Fourier transform. The TWNDOW command o￿ers four weighting algorithms that gradually reduce the amplitude at the ends of the source-trace array to zero.

The TWNDOW command formats trace arrays with one of the four algorithms: HANNING, HAMMING, UNIFORM, and FLATTOP. Each simulates a series

of equally spaced ￿lters. The detected, spectral line traces the top of the passband while moving from N 1 f to (N+1) 1 f.

Hanning, Flat Top, and Uniform Trace Windows (Hamming not shown)

The amplitude and wavelength uncertainty of the Fourier-transformed display depends on the choice of trace windows, and the analyzer sweep time. Amplitude uncertainty is maximum when the spectral component falls midway between the ￿lter shapes. (See preceding ￿gure.) Passbands that are ￿atter in shape, like the FLATTOP ￿lter, contribute less amplitude uncertainty, but wavelength resolution and sensitivity are compromised.

The UNIFORM window algorithm has the least wavelength uncertainty and greatest amplitude uncertainty. Its worst case accuracy uncertainty is 03.9 dB and its 3-dB resolution bandwidth is 60% of the HANNING bandwidth.

The UNIFORM window does not contain time-domain weighting and leaves the data alone. Use it for transforming noise signals or transients that decay within one sweep time period. The UNIFORM window yields the best

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