High-pass filter cut-off frequency
Although the shear probe inherently senses only zero-mean fluctuations, its electronics may impart a non-zero mean that should be removed by digital high-pass filtering. Once the data have been cleaned by removing shear anomalies, it can be filtered. The cutoff frequency for digital high-pass filtering must be decided at this stage. The recommended high-pass filter is a first-order Butterworth filter, applied forwards and backwards, with a cutoff frequency of approximately one-half of the lowest frequency resolved by the spectra for dissipation estimates. The lowest frequency resolved is [math]\displaystyle{ f_l = \tau_{fft}^{-1} }[/math], where [math]\displaystyle{ \tau_{fft} }[/math] is the length of the FFT segments (in s) (add link to fft segment). Thus, the recommended choice for high-pass filtering of the shear data is [math]\displaystyle{ f_{HP} = \tau_{fft}^{−1}/2 }[/math].
Additional information
The shear probe does not respond to a constant cross-axis velocity. It typically responds to fluctuations of cross-axis velocity with a frequency of 0.1 Hz and higher. Additionally, high-pass filtering should be applied to minimize the spectral content of the data at frequencies lower than the frequency resolution of the spectrum, which equals the inverse of the duration of the fft-segments. Thus, if [math]\displaystyle{ \tau_f }[/math] is the duration of an fft-segment, then a good choice is a first-order Butterworth high-pass filter with a cutoff frequency of [math]\displaystyle{ 0.5\, \tau_f^{-1} }[/math] to [math]\displaystyle{ 1\, \tau_f^{-1} }[/math]. The spectra should be corrected for this high-pass filter.
For cases where there is vehicular motions with frequencies at or slightly above lowest wavenumber of spectral resolution, the cut-off frequency of the high pass filter could be increased to suppress the shear-probe signals induced by these motions. However, the final spectrum of shear must be adjusted upwards to account for the high-pass filtering. Hopefully, such undesirable motions will be detected by the accelerometers or vibration sensors on your instrument and will be removed by the Goodman vibration-coherent noise removal algorithm.
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