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Converting between Sine Amplitude and PSD

If you are doing sine-on-random mixed mode testing, it is often useful to be able to convert between PSD and sine amplitude and vice versa.

The following simple formulae can be used:

To convert sine peak to PSD

and to convert PSD to sine peak


= sine wave peak amplitude
= sine wave measured PSD
= frequency resolution of the FFT in Hz

As an example consider you are generating a 2.5 g sine tone and want to check its amplitude on a measurement channel that is displaying a PSD result. The frequency range for the random is set to 3200 Hz with 800 line resolution, hence the frequency resolution is

The expected PSD amplitude for a 2.5 g sine tone would be


To reduce errors in signal processing and thus increase accuracy, we recommend applying an RMS method as implemented in our m+p VibControl software.