# How to get RMS to Frequency chart for discrete samples of acceleration?

I’m reading a book on Motorcycle dynamics and want to compare the vibration profile of my motorbike against this chart:

I am not sure how to get the RMS of acceleration at different frequencies.

I have a mobile phone with an accelerometer that samples acceleration at 100 Hz. I get filtered values of vertical acceleration from external sources (no gravity component).

I can do a Fast Fourier Transform (FFT) of 512 samples of data to get 256 amplitudes of waveforms for a short window of collected data. FFT contains frequencies 1-50Hz

Or I can square each accelerometer output, making them all positive, add them together and take a square root to get a single RMS value. In this case I’m not sure how to get the frequency component of these values.

Can someone help me understand how I get the chart like above from a continuous set of accelerometer output?

Here’s my attempt at plotting the log of amplitude of the FFT (in blue 0-50Hz). I don’t see any dominant component within the FFT output: at the same time the yellow chart above registers acceleration spikes over 0.155(g) threshold. I can see individual impacts on the suspension within the yellow chart, but am not sure how to get their frequency (impacts per second)

I also see this suggestion, but the octave example is not very clear. Is this relevant to my question?

Usually these limits versus frequency are also normalized to be per Hz bandwidth. The FFT noise bandwidth is 1 bin (without further windowing which is another topic of importance if you start seeing dominant tones). So if you sample at 100 Hz with 512 bins, then each FFT bin has a noise bandwidth of $$100/512= 0.1953$$ Hz. A more accurate measurement would average the power (the complex conjugate multiplication of the normalized FFT) over 5.12 bins before taking the square-root to get the average rms value per Hz bandwidth. A simpler and more conservative approach (will bound the actual max limit) would be to multiply the power in each bin by 5.12 before taking the square-root.