Basic FAQ for FFT Analyzer

Parameters representing the state of a vibrating object include acceleration, velocity, and displacement, and as is well known, these are related to calculus. Since accelerometers are commonly used for vibration measurement, FFT analyzers are equipped with integration functions to convert measured acceleration values into velocity or displacement. Also, when acceleration values are calibration in ^{m/s units} of 2, integration allows automatic direct reading of velocity units in m/s and displacement in m. The calculus function of FFT analyzers includes two functions: calculation on the frequency axis and calculation on the time axis.

In the narrowband analysis of power spectrum, the power at each frequency can be considered equivalent to the square of the amplitude of the sine wave, so frequency-axis calculus with the FFT analyzer is performed by multiplication and division of the angular frequency ω (= 2π f, f: frequency). In the integration example, the value of the power spectrum is calculated by dividing the value of the power spectrum by ω ² for single integration and ω ⁴ for double integration (for linear spectra, ω and ^{ω 2} are equivalent). If you only want to find the amplitude value along the frequency axis, frequency calculus is commonly used.

Time-axis calculus directly calculates the time waveform by preprocessing numerical operations, then FFT to obtain the power spectrum. By using time-axis integration, it is possible to determine the time waveform of velocity and displacement from the acceleration waveform, especially the instantaneous amplitude of shocking vibration waveforms.

One thing to note about time-axis integration is that integration operations (especially double integration) require a large numerical dynamic range, so even if you integrate a time waveform with a wide frequency band, it will only be a low-frequency waveform, and the high-frequency waveform will not be practically observable. Specifically, a method involves using a high-pass filter (analog or digital) to time integrate a time waveform with bandwidth restrictions on the frequency of interest.

 

	Frequency Axis Calculus (Basic Terminology Collection for FFT) Time Axis Calculus (Basic Terminology for FFT) Regarding calculus (FFT Analyzer FAQ)