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EQ theory

I have experimented with the EQ of Izotope Ozone to apply an exact inverse equalization of my speakers' lower frequency response plot:



The input signal is first attenuated 10db to prevent clipping. 24 bit instead of 16 bit output should allow this without loss of resolution. A steep and massive 10db bass boost at 30 hz, modeled exactly against my speakers roll-off, is supposed to precisely extend the lower bass range. The two dips at 51 and 142 Hz should further flatten the bass frequency curve:



Ozone includes very good analog model EQs, which I have used for this, and excellent digital linear phase EQs, which I would have preferred instead but aren't usable for some reason. Strangely I can only set the required digital filter steepness at higher frequencies, but not in the lower bass range. Maybe we have an expert around. Is there a mathematical limitation for phase preserving digital filters in the lower frequency range? Or is this a limitation of Ozone?

So far I'm really very satisfied with the results. I took great care not to overdo anything and just add as much as required. A lot of music sounds really substantially better and I haven't found anything sounding worse, yet. But it would be even better if I knew that I could work completely without touching the signal's phase. So share your thoughts if you know anything.

If you want to try this yourself, it's probably better to restrict usage to lossless tracks, because the EQ could raise usually masked artifacts above the threshold of hearing.

I think this shouldn't really mess with dithering too much, which should be mostly hidden in higer frequency ranges. Any other opinions on that?

EQ theory

Reply #1
It will be better if you post your question at the KVR Audio Plug-in forum. Izotope Ozone 3 & 4 has lots of pro-audio users, developers, and support on KVR.

Also Izotope Ozone's lead developer, Alexey Lukin, is a member of the KVR forum so I'm sure he can answer your question directly. Ask for Alexey Lukin.

Here is the link to KVR forums:  http://www.kvraudio.com/forum/viewforum.php?f=6


EQ theory

Reply #2
Thank you! I didn't know that forum, yet. Very insightful!

Edit: I found the anwer just by reading it. They are discussing this a lot. After reading into the right vocabulary at KVR (fir, fft, pre-ringing, etc.) Google found an interesting thread at HA, too:

Discussion between Frank Klemm and DSPguru.

I consider the question solved. I'll stay with the "analog" filters. Any other approaches or criticism are of course still welcome.

EQ theory

Reply #3
Strangely I can only set the required digital filter steepness at higher frequencies, but not in the lower bass range. Maybe we have an expert around. Is there a mathematical limitation for phase preserving digital filters in the lower frequency range? Or is this a limitation of Ozone?

The filter steepness in the low freqs is very probably limited by the filter order used. There are reasons for keeping the filter order low, like keeping computational complexity down and reducing ringing.

Quote
But it would be even better if I knew that I could work completely without touching the signal's phase.

What Frank Klemm points out in the thread linked above is that it might be a better idea to accept a non-linear phase filter for less pre-ringing.

Quote
If you want to try this yourself, it's probably better to restrict usage to lossless tracks, because the EQ could raise usually masked artifacts above the threshold of hearing.

Wrong, since masking calculations assume a linear playback device, and by your EQing you are getting your speakers to be more linear (for on-axis frequency response at least).

regards

EQ theory

Reply #4
Strangely I can only set the required digital filter steepness at higher frequencies, but not in the lower bass range.

When EQ is in Digital mode, its frequency resolution is set by the "EQ Filter Size" control from the Ozone options panel. Increase the filter size to improve steepness at low frequencies.

Response of loudspeakers at low frequencies is usually very room-dependent and has little relation to the passport response measured in the anechoic chamber. So, I'd be careful with excessive amounts of correction: it can significantly narrow the sweet spot. A steep low-frequency cutoff suggests that the loudspeaker has a bass-reflex enclosure, i.e. is already "filtered" to get most from its low-frequency capabilities.

EQ theory

Reply #5
I have experimented with the EQ of Izotope Ozone to apply an exact inverse equalization of my speakers' lower frequency response plot:



The input signal is first attenuated 10db to prevent clipping. 24 bit instead of 16 bit output should allow this without loss of resolution. A steep and massive 10db bass boost at 30 hz, modeled exactly against my speakers roll-off, is supposed to precisely extend the lower bass range. The two dips at 51 and 142 Hz should further flatten the bass frequency curve:




You should be careful about boosting the low frequencies below your loudspeaker's port resonance (40Hz in your case, indicated by the dip between the two bumps on the impedance (blue) line on the graph). The reason is that the cone has to move much further to produce low frequencies at the same level as high frequencies, the lower the frequency the greater the excursion*. In a ported speaker there is nothing to stop the speaker being damaged by moving too much. Also the additional movement required to produce the increased bass can add distortion and reduce mid-range clarity. Given that our ears are less sensitive at low frequencies and that there is not much musical content at 30Hz for many styles of music, I would suggest removing the 10dB boost at 30.5 Hz for safety reasons, if nothing else.  If you are really keen, you could try ABXing with and without the boost to see how audible it is.

* In ported speakers the cone actually moves less at the resonant frequency of the port, but excursion increases as frequency decreases below resonance.

EQ theory

Reply #6
Thank you all for your insightful comments!

Alex, I had already tried increasing the filter size. Still it's impossible to get the linear phase filter as steep for the low bass range as seen in the picture. I have been convinced (by sound & theory) that Ozone's minimum phase "analog" EQ is better for my purpose, so that's ok. It's working out excellently. Is it a biquad implementation?

You should be careful about boosting the low frequencies below your loudspeaker's port resonance (40Hz in your case, indicated by the dip between the two bumps on the impedance (blue) line on the graph). The reason is that the cone has to move much further to produce low frequencies at the same level as high frequencies, the lower the frequency the greater the excursion*. In a ported speaker there is nothing to stop the speaker being damaged by moving too much.


The two bass drivers are rather small (18cm), but have a large maximum excursion of about 3 cm (+/-15 mm). The cones are rigid aluminium sandwiches. The maximum nominal power is three times that of my amp. So I wouldn't expect that I could damage them by this.

Also the additional movement required to produce the increased bass can add distortion and reduce mid-range clarity.


You seem experienced in this. How high would you assess the probability for that happening? The speakers are usually very stingy with any distortion, wether harmonic or anything else, almost overanalytical.

Given that our ears are less sensitive at low frequencies and that there is not much musical content at 30Hz for many styles of music, I would suggest removing the 10dB boost at 30.5 Hz for safety reasons, if nothing else.  If you are really keen, you could try ABXing with and without the boost to see how audible it is.


I ABX'd the whole setting (including the two additional dips) for a large range of music with my girlfriend. Ozone includes a level matched bypass button well suited for this. A lot of pop music doesn't make any difference and seems to be high passed. But contemporary jazz like Esbjörn Svensson is actually quite easy to distinguish and really sounds better with a more powerful base.

Of course it's hard to judge. Louder often sounds better on the first look. Although it's level matched, the EQd signal contains more energy after all. I'm thinking about making this my general listening setting. I also thought about even going up to 15db boost. I'm not experienced enough though to assess the risk of mid range distortion for the thousands of tracks that I haven't tested, yet.

EQ theory

Reply #7
Yes, it's a standard biquad implementation.

EQ theory

Reply #8
The two bass drivers are rather small (18cm), but have a large maximum excursion of about 3 cm (+/-15 mm). The cones are rigid aluminium sandwiches. The maximum nominal power is three times that of my amp. So I wouldn't expect that I could damage them by this.


Quote
You seem experienced in this. How high would you assess the probability for that happening? The speakers are usually very stingy with any distortion, wether harmonic or anything else, almost overanalytical.


It is hard to say how likely this is to happen. There are too many factors (the frequency and level of the original music, how loud you listen to it, the properties of the speakers themselves).

It may be that it is not a problem for you, in your particular circumstances.  If you see the cones moving a lot, or more than normal, be careful.

Here is a rough idea of what happens in a ported speaker.



EQ theory

Reply #9
Thanks, Iain!



I understand now why you were calling for caution. The increase below the port resonance is really quite steep even despite the frequency roll-off. Seeing that, I'm not so shure anymore that I couldn't grill them with a 10hz test tone with a much weaker amp than their rated power.

I'm wondering what a plot with current depth of excursion on the x-axis and ability to concurrently play frequency n without distortion on the y-axis would look like, n being the highest frequency that a driver is responsible for in a multi path setup. Would that rather be a flat line with sharp roll-offs near the maximum recommended excursion depth or gradually falling off from the the neutral position?

In the latter case my push beneath the port resonance would surely have some impact onto the higher frequencies. The former case would mean that it could work out without distortion as long as I stay within certain safe limits.

Of course the exact shape of such a plot would be very driver dependent. But maybe the shape of the curve could be generalized like in your last image?

 

EQ theory

Reply #10
Thanks, Iain!

I understand now why you were calling for caution. The increase below the port resonance is really quite steep even despite the frequency roll-off. Seeing that, I'm not so sure any more that I couldn't grill them with a 10hz test tone with a much weaker amp than their rated power.

I'm wondering what a plot with current depth of excursion on the x-axis and ability to concurrently play frequency n without distortion on the y-axis would look like, n being the highest frequency that a driver is responsible for in a multi path set-up. Would that rather be a flat line with sharp roll-offs near the maximum recommended excursion depth or gradually falling off from the the neutral position?

In the latter case my push beneath the port resonance would surely have some impact onto the higher frequencies. The former case would mean that it could work out without distortion as long as I stay within certain safe limits.

Of course the exact shape of such a plot would be very driver dependent. But maybe the shape of the curve could be generalized like in your last image?


I'm not sure what you are asking for but perhaps this will help.

Loudspeakers are limited by two main things: 1) power handling, if you exceed the maximum power a speaker can handle the voice coil melts like a fuse; 2) Cone excursion, if you push the cone too far you get distortion. Even further and you may rip the cone, surround, spider etc, or the voice coil may pop out of the magnet gap, or slam backwards into the back-plate and get damaged.

So the maximum SPL a ported speaker can produce without producing distortion looks like this:



Also, you speakers may have a High Pass Filter in the crossover to prevent sub-sonic frequencies from causing problems, this was common when vinyl records were much more common though. A warped record could easily produce some 1-5Hz signal.

 
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