audio HP and LP filter cutoff frequencies

Thread Starter

ebeowulf17

Joined Aug 12, 2014
2,971
Hey everybody, I'm working on some audio post production work right now, using PreSonus Studio One. I wanted to use a high pass on one channel and a low pass on another in such a way that I could then combine them without emphasizing or de-emphasizing any particular frequencies - it's sort of like a crossover in reverse.

Anyway, the weird thing that came up, is that if you choose different filter slopes in Studio One, the frequency you've chosen ends up being attenuated by different amounts. My experience up until now has been that EQ settings, filter cutoffs, microphone specs, etc. are pretty much all described based on their 3dB down points. So, I would've expected a 150Hz HP filter to be 3dB down at 150Hz, regardless of the chosen slope. As it is, one slope yields the expected -3dB at 150Hz. Two of the slopes yield -6dB at 150Hz, and one yields -9dB at 150Hz.
PreSonus-Studio-One-HP-freq.png
PreSonus-Studio-One-HP-freq2.png
Am I missing something, or is this really strange? At first I thought maybe these filters were being described in terms of the cutoff frequency of a single pole, and then had different responses because of the additional poles, but that doesn't seem to add up either.

Another interesting thing that I discovered is that the filters which are 6dB down at 150Hz can be used, in conjunction with a 150Hz LP filter, to achieve my "reverse-crossover" system with near-perfect results... but the filter which is 3dB down at 150Hz behaves unexpectedly. I'd expect the combo of two channels that are down 3dB at 150Hz to result in a signal that boosted 3dB at 150Hz. Instead, the result is a perfect null at 150Hz. I'm guessing that this filter has a 90 degree phase shift at the 3dB down point, and that combining two filters with a +90 and -90 phase response results in perfect cancellation.
PreSonus-Studio-One-HP-output-6-or-24dB-octave.png
PreSonus-Studio-One-HP-output-12dB-octave.png
So, in terms of accomplishing what I need to musically, I can just use the 6 or 24dB/octave filters and get the desired results, but I'm very curious about the naming/labelling of these filters, and the apparent phase response implications, with one filter cancelling completely and two other filters appearing to work perfectly.

Any thoughts? Am I wrong to expect these filters to be described by their 3dB down point?
 

Audioguru

Joined Dec 20, 2007
11,251
Simply adding filters in series also adds the -3dB losses. You need 2nd order, 3rd order, 4th order etc Butterworth filters so that each produces -3db at the cutoff frequency.

Highpass and lowpass Butterworth filters with even orders cause cancellation at the cutoff frequency. Odd orders do not.
Linkwitz-Riley highpass and lowpass filters produce -6dB at the cutoff frequency and all frequencies are in phase.
 

Thread Starter

ebeowulf17

Joined Aug 12, 2014
2,971
Thanks for the explanations. I'd already tried looking at several websites that discuss the filter responses, but hadn't quite made sense of it. With your reference points in hand, re-reading several of those sites makes a lot more sense now!

So, it looks like maybe this software is using Linkwitz-Riley filters for the 6dB/octave and 24dB/octave filters, resulting in -6dB at the cutoff frequency and all frequencies in phase (very nice for my crossover needs.)

And I'm guessing the 12dB/octave filter is a two-pole Butterworth, thus the complete cancellation, and the -3dB level at the cutoff frequency.

And just to make sure I'm understanding this correctly, it sounds like high and low pass filters aren't generally described in terms of their -3dB points, but rather by their cutoff frequencies? And further, the relationship between the cutoff frequency and the -3dB point depends on both the filter topology and the number of poles, so it's not something you can make assumptions about just based on filter slope alone?
 

Audioguru

Joined Dec 20, 2007
11,251
Each RC pole produces 6dB per octave which is 20dB per decade.
The cutoff frequency of an RC pole is its -3dB cutoff frequency. In series and buffered from each other their -3dB reductions add for each RC pole.
A Butterworth filter uses a little positive feedback to boost its level at the cutoff frequency up to -3dB.
 
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