Other Limitations of the FFT

The FFT requires that your signal waveform have the same value at start and finish. This requirement is a consequence of FFT time wrapping, which makes the endpoint and beginning point actually adjacent in FFT time.

Another limitation of the FFT has to do with the maximum allowable rate of change for signals represented in discrete time. The Nyquist sampling theorem says that no band -limited signal can transition perfectly from one value to another in one time step without causing ripples in the adjacent samples. For example, if you try to work with a signal that incorporates a step change in signal amplitude at the end of the time window, it will cause ripples in both directions, distorting both the signal at the end of the time window and the samples near the beginning. To solve this problem, make sure the signal amplitude has by design the same amplitude (usually zero) at start and finish.

The normal way of harmonizing the beginning and ending of your excitation signal is to drive the system with a pulse, which first steps up, holds longs enough for you to see the resulting waveform, and then steps back down. After a suitable waiting interval, the system will have stabilized and the FFT time window may come to a close with zero excitation . The total FFT time window must therefore exceed the pulse duration plus one system stabilization time. I usually make the pulse duration half the width of the FFT time window and ensure that the total FFT time window exceeds twice the system stabilization time.

POINT TO REMEMBER

• The FFT requires that your signal waveform have the same value at start and finish.