I am currently working with vibration measurements in structures. In the netherlands there is a guideline for verifying vibration measurements for damage to machinery. This is the so-called "SBR Trillingsrichtlijn". In this guideline a frequency weighting function is specified to modify the time series from vibration measurements:
with small f being the frequency in Hz, f_0 a constant frequency of 5.6 Hz and v_0 a predefined constant velocity of 1 mm/s. To illustrate the filter behaviour i show it graphically here as well (axes are linear):
In post-processing this is fine as i can perform an FFT on the time series data, apply this weighing function in the frequency domain (through multiplication with the FFT transformed time series) and then do an inverse FFT to get the adjusted time signal data.
My question is the following: the equipment we use to measure vibrations does this weighing internally using a digital filtering on the time series in real-time. To verify the data i would like to design a digital filter corresponding to the weighing function above, can anyone point me to a resource how to approach this? From what i have looked up so far on IIR / FIR filter design usaully the examples start from a transfer function in the s-domain or z-domain (which correspond to a laplace transform in discrete or continuous time) but now i only have a frequency response in the fourier / frequency domain.
EDIT: Based on suggestion of @Hilmar it appears a simple first order high pass function. i made a python implementation to check the method of FFT and the highpass filter. shown in the graph here. Strangely the frequency response of the highpass filter and SBR specified response match exactly but the implementation using the highpass has some artefacts whereby non existant frequencies are generated with non-zero amplitudes:
this can be seen in the green dotted line which is a mock signal filtered in python using the scipy package.