low pass filter design for accelerometer
Y[n]=aX[n]+(1-a)Y[n-1]

It's an autoregressive moving average-- an infinite impulse response filter.  Start with the equation above, take the z transform, and that gives the frequency response.  It has nothing to do with the noise model.

Here's the freq response for alpha =0.9, the frequency axis is scaled from 0 to your Nyquist frequency (half your sampling freq) generated in Octave by freqz(0.9, [ 1 -0.1])



alpha=0.6
freqz(0.6, [ 1 -0.4])