Page 35 - Shock and Vibration Overview

Analysis Overview

identify the major frequencies that exist to help the analyzer determine the cause of
any vibration signal.

Windowing
Fourier transforms perform an integral from negative infinity to positive infinity; but
one can only acquire data over a discrete time period. So a Fourier transform must
repeat the signal infinitely to perform the transform. When the acquired data begins
and ends at 0, or if there are an integer number of cycles, then this infinite repetition
will cause no problems. But if these are not true, there will be leakage in the

frequency domain because the signal is distorted as shown in Figure 18.

Figure 18: The time-window effects are shown when using a FFT analyzer without windowing (or
rather a uniform window) are shown. (A) represents an integer number of cycles so that the
spectrum has a clear spectral line. (B) and (C) represent time signals where there are a half
integer number of periods, but with different phase relationships, which gives a different
discontinuity and spectral leakage.

Remember that a Fourier transform looks to calculate a series of sine waves to
represent the data. If there is a discontinuity in the data (by not beginning and
ending at 0 or not having an integer number of cycles) then the FFT analyzer will
need many terms to approximate the apparently discontinuous signal.

In order to minimize this error, windows are used to better make the signal appear
periodic for the FFT process. The most common windows are the rectangular
window, the Hanning window, the flattop, and the force/exponential window (used

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