# how to convert SPL in dBA to dB

I wonder how I can convert dBA (A weighted) to dB and vice versa. can anybody provide any kind of table or online conversion app? thanks

following formula comes from https://en.wikipedia.org/wiki/A-weighting :\begin{align} R_A(f) &= {12194^2 f^4 \over \left(f^2 + 20.6^2\right)\ \sqrt{\left(f^2 + 107.7^2\right)\left(f^2 + 737.9^2\right)}\ \left(f^2 + 12194^2\right)}\ ,\\[3pt] A(f) &= 20\log_{10}\left(R_A(f)\right) - 20\log_{10}\left(R_A(1000)\right) \\ &\approx 20\log_{10}\left(R_A(f)\right) + 2.00 \end{align} how can I inverse this formula? I also must mention that I have a specific frequency and I just want to convert this specific frequency SPL

• this has nothing to do with filter-design,kalman-filters, digital, and only kind of something with filters. – Marcus Müller Feb 22 at 13:47
• Do you have a single SPL value, or SPl values for the whole spectrum? – Justme Feb 22 at 18:37
• @Justme. just single value – SeAlGhz Feb 27 at 19:48
• @ali if you have a single value, and no information about the frequencies present in the signal, it cannot be known how it is converted between unweighted and A-weighted values, as it depends on the frequencies present in the signal. – Justme Feb 27 at 20:04
• @ali Why did you not say earlier then, that detail is important and should be edited in the question. The formula gives you the weight at any frequency. So if you have a single frequency, you can calculate the weight at that single frequency. And since you know the weighted value and how much the value was weighted, you can also know what was the unweighted value. – Justme Feb 27 at 20:21

## 1 Answer

You can't convert these directly. You need to start with either a calibrated pressure time domain pressure wave form or a calibrated power spectrum. To create calculate unweighted dBSPL yo simply sum the total energy. To calculate dBA, you need to apply an A-weighting filter to either one of those first.

• how can I calibrate ADMP401 precisely do you know have any idea? – SeAlGhz Feb 22 at 15:26
• With a good measurement microphone and a matching calibrator. You use the calibrator to calibrate the measurement mic and then the measurement mic to calibrate the ADMP401. It also depends on what exactly you mean by "precisely". +1dB is very different from +- 0.1dB – Hilmar Feb 22 at 16:31