FFT Analyzer Basic FAQ

​Acceleration, velocity, and displacement are parameters that describe the state of a vibrating object, and as is well known, these are related by calculus. Since Accelerometer are commonly used as vibration measurement sensors in practice, FFT analyzers are equipped with integration functions to convert measured acceleration values into velocity and displacement. Furthermore, if the acceleration value is EU calibration in units of m/ ^s², the velocity can be automatically read directly in units of m/s and the displacement in units of m by integrating. The calculus function in the FFT analyzer has two functions: calculus on the frequency axis and calculus on the time axis.

In a narrowband power spectrum analysis, the power at each frequency can be considered equivalent to the square of the sine wave amplitude. Therefore, frequency-axis differentiation in an FFT analyzer is performed by multiplication or division by the angular frequency ω (= 2πf, where f is the frequency). In the example of integration, the power spectrum value is obtained by dividing by ^ω² for single integration and by ^ω₄ for double integration (equivalent to ω and ^ω² in a linear spectrum). Frequency differentiation is often used when only the amplitude value on the frequency axis needs to be determined.

Time-domain calculus involves directly pre-processing the time waveform numerically, and then performing an FFT to obtain the power spectrum. By using time-domain integration, it is possible to determine the time waveforms of velocity and displacement from the acceleration waveform, and in particular, to read the instantaneous amplitude of shock vibration waveforms.

One thing to be aware of with time-axis integration is that integration operations (especially double integration) require a large numerical dynamic range. Therefore, even if you integrate a time waveform that includes a wide frequency band, you will only get a waveform in the low-frequency band, and the waveform in the high-frequency band will not be practically observed. A specific method is to use a high-pass filter (analog or digital) to limit the time waveform to the frequency of interest and then integrate the resulting time waveform.

 

	Frequency axis calculus (FFT basic glossary) Time axis calculus (FFT basic glossary) Regarding differential and integral calculus (FFT analyzer FAQ)