## Filter slope and roll off freq add up?

1

Here's a little something that puzzles me; do I add up the roll off point (-3db) to the attenuation per octave (eg. 18dB/va) or not?

Am I correct that the roll off point is not to be considered important when calculating the attenuation?

My test: Protools and Waves Q1, Rchannel,EQ3 filters

signal generator at 300Hz at 0dBFS
highpassfilter is set at 300Hz
result in level: -3dBFS

signal generator at 150Hz at 0dBFS
highpassfilter is set at 300Hz
result in level: -18dBFS

signal generator at 75Hz at 0dBFS
highpassfilter is set at 300Hz
result in level: -36dBFS


Conclusion: slope at 18dB/va So far so good! (with Q1 the slope is 12dB/va with corresponding results btw)

Now this: Used: Protools and Scheps 73 and VEQ3

signal generator at 300Hz at 0dBFS
highpassfilter is set at 300Hz
result in level: -3dBFS

signal generator at 150Hz at 0dBFS
highpassfilter is set at 300Hz
result in level: -21dBFS

signal generator at 75Hz at 0dBFS
highpassfilter is set at 300Hz
result in level: -39dBFS


Both the 1 oct down and 2 oct down do differ with the first test, they have 3 dB extra? Has this to do with the rolloff point (an extra 3dB) or is it something else?

3

You don't add the rolloff point. The attenuation per octave is only asymptotic, the rolloff point is "half" in the pass band. It's where the asymptote would cross the passband line, but the actual frequency response passes 3dB below the passband.

See below:

Notice the corner cut out at the cutoff frequency between the red curve and the straight blue lines. Where the blue lines meet would be 0 dB attenuation if the filter were "perfect". Far enough above the cutoff frequency, the real attenuation and the "perfect" attenuation are very close, so the actual attenuation is almost exactly what we would calculate by starting at 0 dB and subtracting 18 dB per octave. The 3 dB drop at the cutoff frequency is an "error" of sorts caused by the behavior of real world filters.

I've gotta give an upvote for an answer that sounds just so right, yet I didn't understand a single, solitary word of ;) – Tetsujin – 2017-12-20T12:44:40.497

That's what I thought indeed, do not add the roll off point. Thanks for confirming. – user3810130 – 2017-12-20T14:09:10.043

@Tetsujin Look at this graph: https://en.wikipedia.org/wiki/Low-pass_filter#/media/File:Butterworth_response.svg The 3 dB that you don't add are shown in the gap between the actual response curve in red and the idealized straight lines in blue. The red line approaches the sloped blue line asymptotically, which is what this answer means by "the attenuation per octave is only asymptotic".

– Todd Wilcox – 2017-12-26T19:43:03.173