Dynamic signal analyzers use Fast Fourier transforms (FFTs) to process and deliver frequency information; an FFT generally works with a group of samples of equal time duration. These samples fall within the time record, a “snapshot” of the continuous wave. But to process and analyze the data effectively, additional mathematical manipulation may be needed.

When measuring repetitive signals (like sine waves), the time record generally encompasses numerous cycles. Ideally, the time record is of a duration that grabs an exact integer number of cycles – the wave will begin and end at a coincident point. In reality, it is often difficult to get the input function to be periodic in the time record, as the ideal situation is called.

An effective FFT of such a wave relies on the appearance of continuity for all time. If the time record begins and ends at different points on the cycle, the wave appears discontinuous; tying the front of the sample to the back (emulating a lack of interruption) will result in jump discontinuities, with a cusp or a total separation in the waveform.

To mitigate the influence of discontinuities, window (or weighting) functions are imposed on the waveform, framing it within the time record so that it complies with the FFT’s interpretation of continuity; the window focuses the FFT away from the edges of the sample, where the discontinuity is observed.

The most common is called a Hanning window. It multiplies the signal amplitude by zero at the beginning and end of the time record, and the multiplier gradually peaks toward the center. This serves to give high resolution (determination of frequency) when time records are imperfectly matched to the signal. But amplitude readings deteriorate somewhat, since the Hanning function immediately slopes away from the middle of the record, leaving little room to recognize the full amplitude.

A similar method, the flat top, also begins and ends at zero amplitude, but increases to a plateau, peaking across a wider range than the Hanning window. Amplitude readings are strengthened appreciably, but resolution suffers, since the “filtering” effect of the window combined with the FFT is widened toward the edges of the time record, and subtle frequency components sometimes get drowned out as the stronger components are “smeared” across a broader band.