Please also refer to the following past columns.
Fundamentals of Digital Signal Processing - 4 "Power and Power Spectrum of Time-Domain Signals"
Fundamentals of Digital Signal Processing - 8 "Various Power Spectra"
In an FFT analyzer, the Overall Value (OA value) refers to the combined power across the entire analysis frequency band obtained by calculating the power spectrum of a time signal such as sound or vibration using FFT. Specifically, it is displayed as a triangular mark in the upper right corner of the power spectrum graph, as shown in Fig. 1.
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Fig. 1 Display method of OA value (Overall Value)
Here, if we let the input signal be x(t) and its power spectral density function be G(f), then from Parseval's formula or the definition of the power spectral (density) function:
There is a relationship between them (a strict explanation is omitted). ① The right-hand side of the equation corresponds to the OA value, so the physical meaning of the OA value is "corresponding to the mean squared value (or power) of the input signal x(t)".
For specific instructions on how to calculate the OA value in an FFT analyzer, please refer to the relevant page "Overall" in the "Glossary of Basic Terms Related to FFT Analysis" on our website.
Overall - Glossary of Basic Terms Related to FFT Analysis
To elaborate slightly, if the power spectrum P(f) is given by ΣP(f), then it becomes (ΣG(f))Δf.
OA values can be expressed numerically in two ways: logarithmic (dB) and linear. Linear representation is further divided into power (mean square) and its square root, the RMS value. In addition to the power for the entire analysis frequency range, it is also possible to calculate a partial overall value (POA value) limited to a specific frequency band.
Next, what is the relationship between the output results from sound level meters and vibration meters and the OA values from the FFT analyzer? Please refer to Fig. 2, which is an addition to the information provided in the previous newsletter.
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Fig. 2 AP value and OA value
The value obtained by directly calculating the RMS value of the AC signal from a sensor without frequency analysis is sometimes called the Allpass Value (AP value). For a steady-state signal, the AP value and OA value will be approximately equal. In octave analysis, a common analysis method in acoustics, both values are sometimes displayed simultaneously. (Example from our DS-2000 series: Fig. 3)
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Fig. 3 AP and OA values in octave analysis
If there is a clear difference between the AP value and the OA value, the frequency band should be considered. For example, when comparing the OA value obtained by analyzing the AC output of a precision sound level meter in a 10kHz bandwidth with the display value (AP value) of the sound level meter, a clear difference will appear if there are relatively large signal components in the frequency band above 10kHz.
The main advantages of using OA values are as follows:
- Since the frequency band can be clearly defined and determined (calculation of the POA value), if the calculation method is the same, almost the same results can be obtained even if the model or manufacturer is different.
- Even when analyzing an AC signal with flat frequency weighting, it is possible to calculate frequency-weighted data, such as A-weighting, through post-processing.
Finally, I will discuss the calibration of sound and vibration levels using a frequency analyzer.
Generally, for the physical calibration of sound and vibration, the calibration signal of a single sine wave output from the calibrator is analyzed using the FFT.
The value is input into an analyzer or similar device, read, and converted into a calibration value.
Regarding how to read the values, I recommend using the OA value from an FFT analyzer for the following reasons. (This is my personal opinion.)
- Sound level meters and vibration meters do not read the level of a single sine wave; rather, they display the AP value, and the OA value, which is its equivalent, is more appropriate.
- Due to the influence of the FFT analyzer window, bias errors occur in the peak level of a single sine wave. Reading the OA value can help avoid these errors.
(See previous columns below)
Fundamentals of Digital Signal Processing - 7 "Spectrum and Time Window"
Of course, point 2 can be similarly avoided by using windows such as flat tops.
(Excerpt from the email newsletter issued on March 25, 2008)
