I am trying to make a 3dB/oct High-Pass Filter, maybe it can call "half-order"?
Because as I know the basic order for the first-order filter is 6dB/oct, but how can I make a 3dB/oct filter?
here is the 200Hz 6dB/oct High pass filter:
but how to make 200Hz 3dB/oct High pass filter, which slope is more gentle than the 6dB/oct.
The first obvious thing I can think of is to take the square root of the transfer function as power series, truncated to a sufficiently large number of terms, and implement that as a FIR filter. The problem is that the number of terms required to get a good approximation may be prohibitively expensive, especially for a low cut-off frequency. I've computed the first 10240 terms of the filter you requested using this method, but I haven't analyzed it to check if it's a decent approximation (let alone after truncating it to a more reasonable length).
You can trick a low-shelf filter into approximating your desired response. By setting its fo = 26 Hz, slope factor = 0.21, and boost = -25 dB, you get the result shown below -- a highpass whose -3 dB point is near 200 Hz, with a 3 dB / octave (10 dB / decade) slope down to below 3 Hz:
Note that the stock shelf filter only allows for a -10 -- +10 dB boost, so I calculated the needed coefficients with the attached spreadsheet, then typed them manually into the filter as shown above. Small coefficient changes result in large response swings, suggesting that double-precision arithmetic should be used.
Hello matthijs and Bob,
Thanks you guys for replying me!
I will do some testing with this method!