NIST Technical Note 1337: Characterization of Clocks and Oscillators

FIGURE 10.6eliminates discontinuities due to the ends ofsample length T.Each time the Hanni ng wi ndow is app 1i ed, theside lobes in the transform are attenuated by 32aB/octave, and the main lobe is widened by 2tl.f.The amp 1itude uncertainty of an arbitrary sinewave input is reduced as we increase the number ofHanns; however. we trade off reso1ution in frequency.The effective noise bandwidth indicates thedeparture of the fi 1ter response away from a truerectangularly shaped filtered response (frequencydomain). Table 10-1 lists equivalent noise bandwidth corrections for up to three app 1i cati on5 ofthe Hanning window. 11Number of HannsEquivalent NoiseBandwidth1 1.5 af2 1.92 Af3 2.31 AfTABLE 10. I10.6 Picket-Fence EffectThe effect of leakage discussed in the previoussection gives rise to a sidelobe type responsethat can be tailored according to thetime-window function through which the analyzedsignal passes as a block to be transformed to thefrequency domain. Using the Hanning window diminishesthe amplitudes of the sidelobes. however, itincreases the effective bandwidth of the passbandaround the center frequency. This is because theeffective time-domain window length is shorterthan a perfect rectangular window. Directlyrelated to the leakage (or sidelobe) effect is onecalled the "piCket-fence" effect. This is becausethe sidelobes themselves resemble a frequencyresponse which has geometry much 1ike a picketfence.The existence of both sidelobe leakage andthe resultant picket-fence effect are an artifactof the way in which the FFT analysis is performed.Frequency-domain analysis using analog filtersinvolves a continuous signal in and a continuoussignal out. On the other hand, FFT analysisinvolves a continuous signal in, but the transformto the frequency domain is performed on blocks ofdata. In order to get di screte frequency i nformationfrom a block, the assumption is made that theblock represents one peri od of a periodi c signa1.The picket-fence effect is a direct consequence ofthis assumption. For example, consider a sinewavesi gna1 whi ch is transformed from a t ime-varyi ngva 1tage to a frequency-domai n representationthrough an FFT. The block of data to be transformedwill be length, T, in time. Let's say that theblock, T. represents only ~ cycles of the inputsinewave as in figure 10.5. Artificial sidebandswill be created in the transform to the frequencydomain, whose frequency spacing equals f, or thereciprocal of the block length. This representsa worst-case condition for sidelobe generationand creates a large number of spuri ous discretefrequency components as shown in figure 10.7(b).If, on the other hand, one changes the blocktime, T. so that the representation is an integralnumber of cycles of the input sinewave, then thetransform will not contain sidelobe leakage compo­33TN-46