Ocean Wave Height Calculation

[vtomanov]

I'm trying to calculate the Ocean Wave Height using FFT and 3 axis accelerometer. My understating how to do it is :

I need to calculate the spectrum of A ( A=sqrt(ax^2+ay^2+az^2)) , by standard FFT function. This will give me the acceleration spectrum, Sa(f), which is the function of wave frequency, f.
To convert it to the more conventional elevation spectrum, Sz(f), I need to divide it by (2pif)^4, because acceleration of the circular wave motion is A=Z*(2pif)^2, while the spectrum is the squared magnitude, Sz~Z^2.

in brief the logic should be 👍

1. the accelerometter returns values between 0 and 4096 ( e.g. the actual 0 is the middle 2048 )

2. read the calibration values
   aX
   aY
   aZ

assuming we need ( -, 0, +) values and the 0 is 2048 we adjust them to :
dX = aX - 2048
dY = aY - 2048
dZ = aZ - 2048

3. calculate the calibration magnitude

cM = sqrt(dXdX + dYdY + dZ*dZ);

4. calculate the coefficient to get the values in m/s

coefMS = 9.83 / cM

-------------- real-time calculations ---------

defaults:

SAMPLES[128]; // 128 values

SAMPLING_PERIOD = 250; // 250 milliseconds - e.g. 32 seconds for 128 values
SAMPLING_FREQUENCY = 4.0; // Hz ( 4 times every second)

calculations :

we assume that maximum wave frequency that we will measure is 30sec ( usually sea waves are about 20 sec max)

collect value for 32 sec every 250millis one value = sqrt(dXdX + dYdY + dZ*dZ) * coefMS; // to get it in m/s

after we get a 32 sec sampling and fill 128 values we use FFT :

FFT.Windowing(...);
FFT.Compute(...);
FFT.ComplexToMagnitude(...);

we calculate the peak

FFT.MajorPeak(...);

it returns peak interpolated frequency - pF and peak value pV

calculate the actual sea wave length in meters :

SEA_WAVE_LENGTH_IN_METERS = pV / ((2pipF)^4);

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Does this sounds right to you ?