THE SCIENCE AND APPLICATIONS OF ACOUSTICS - H. H. Arnold ...

196 9. Sound-Measuring InstrumentationFigure 9.18. Illustration of the picket fence effect. If the frequency coincides with a line,it is indicated at its full level. Otherwise, it is represented at a lower level if the frequencyfalls between the lines.The effect of leakage, or window error, becomes apparent when the power ina single-frequency component appears to leak into other frequency bands. Twoprimary causes exist for window error: (1) the signal is not fully contained withinthe observation window or (2) it is not periodic within the window. The simplestcase is that of a monofrequency sinusoidal wave, which should yield only onefrequency component in the FFT analysis if there are an integral number of periodsof the sine wave in the finite record length. But a nonintegral number ofperiods will generally occur, and the cyclic repetition will yield a signal whosespectrum covers a range of frequencies. Leakage may be counteracted by forcingthe signal in the data window to correspond to an integral number of period ofall significant frequency components through a process called order or trackinganalysis, where the sampling rate is related directly to basic frequency of the noisegenerating process (such as the shaft speed of a machine) and in modal analysismeasurements where the analyzer cycle synchronizes with the periodic excitationsignals.The picket fence effect (Figure 9.18), which is not unique to FFT analysis, occursin any set of discrete fixed filters. The magnitude of the amplitude error occurringfrom this effect depends on the degree of overlap of adjacent filter characteristics,a consideration that influences the selection of a data window.9.14 Data Windows and Selection of Weighting FunctionsIf a steady pure-tone of an unknown frequency were to be analyzed, it wouldusually be sampled over a short-time interval that is termed window duration. Arectangular window will allow passage of a portion of the input signal without adjustment.That short segment obtained is presumably representative of the originalsignal, and this would also hold true if that segment embodies an integer numberof periods of the original signal. The effect of window duration arising from thescanning of (usually) noninteger number of periods is depicted in Figure 9.19.Such a signal would be analyzed as if the segment iterated itself as in the figure.