The attached SoundFile? contains 3 variants of the "SuperEQ", one for mono input, another for stereo, and the 3rd for stereo live input.

What is a SuperEQ? I discovered something very significant about using Butterworth filters the other day... The traditional way to arrange a filter bank is to use a bunch of parallel bandpass filters fed off the input source. But when you do this with bandpass filters created as a cascade of a Butterworth HPF and a Butterworth LPF, you get severe phase cancellation (i.e., notches -- big ones!) at the band edges where one bandpass filter adjoins another.

That is... unless you restrict yourself to 1st order filters. In that case they join almost perfectly. But the problem with 1st order filters is one of selectivity. Too much energy bleeds over from one channel to the next unless you restrict your cuts and boosts to small amounts, e.g., something less than 6 dB. For mastering that is more than enough. But there may be times when you need more cut or boost in one band...

However! If you arrange to feed each successive bandpass off the highpass filter used by the next lower band then you get buttery smooth, fabulous EQ filterbanks, with hardly any phase cancellation, when using 4th order filters. These filters become 8-pole bandpass sections, and have 24 dB/octave rolloff at the band edges. That permits up to 24 dB of cut or boost without significantly affecting neighboring bands.

So these SuperEQ's are 10-band (10 octave) EQ's built from 4th order Butterworth filters, found in the standard Kyma Prototypes. Frequency coverage is from DC to 20+ KHz. The two end filters are just low pass and high pass filters extending all the way to the end of the spectrum. Those in the middle are cascaded 4th order LPF and HPF filters. Band edges were determined as the square root of the band centers. Band centers are at 31.25 Hz, 62.5 Hz, 125 Hz, 250 Hz, 500 Hz, 1 KHz, 2 KHz, 4 KHz, 8 KHz, and 16 KHz.

This SuperEQ sounds creamy smooth to me and others I have shown it to. Enjoy!

-- DavidMcClain - 14 Feb 2004

I compared it with Default GraphEQ. Super EQ don't look as flat as graph in the high range (8k and above). I like the superEQ sharp curve (always compared to Graph). It looks like super EQ is "offset to the right", frequency-wise compared to Graph. I measured EQ response visually with SpectraLab, feeding 5 secondes of Steve Reich "8 lines" and a "white noise"....alternatively. At first touch I like what you did on this one. BTW I'm still trying to understand your Compressive EQ patch!!

- KarlMousseau - 14 Feb 2004

Hi Karl,

Yes, being IIR filters derived from the bilinear mapping from analog space to the digital domain, the actual frequency response of the digital filters will become displaced as you move away from the small angle approximation (SAA) region of frequencies. That's one of the reasons that 96K and 192K are so attractive... they keep frequencies as high as 16 KHz still in the SAA region.

But I find it interesting that you would care that much about flatness above 8 KHz!? Can you really hear the difference? (This isn't an idle question either, since without considerable help, I can't hear anything that high at all.) I do know that humans lack the ability to discern pitches that high up. Instead it becomes more of a sense of "air" and spaciousness -- more of a feeling than of a pitched sound.

The thing that most impressed me about SuperEQ was actually the extended deep bass response. The GraphicEQ? can't compete down there, because it is an FIR filter with only about 100 taps or so. In order to get good filtering from an FIR, it needs to be about 3 wavelenghts long, at least. With only 100 taps, at 44 KHz sample rate, a 250 Hz wave has a wavelength of around 176 taps, which makes the FIR GraphicEQ? insufficient at 250 Hz by a factor of more than 5 times in length.

But using the 4th order Butterworth filters we can go all the way down to 31 Hz and still have decent performance. So I love the luscious, almost infra-sonic, bass enhancements. It doesn't take much boost either, since our Fletcher-Munson response down there is so crowded together. A few dB of SPL makes a huge number of dB HL (hearing level) difference.

The compressive EQ is an idea borrowed from BSS. I ended up getting a BSS Opal (DPR 944) for kicks. It is an analog processor that uses subtractive filtering and compression on a bandpass filter before summing back to the subtracted signal. Unfortunately, the unit as constructed can only do attenuation EQ. In order to achieve the full range of effects you need to use a graphic EQ before or after the unit. I wish I had known that before spending my hard earned on it. But it was an interesting learning experience. -- You really have to watch out for what precisely isn't mentioned!

I think the places where this kind of compressive EQ (attenuation style) is most useful is in supressing sibilance of singers -- sophisticatd de-Essing. When I say "attenuation-style" compression, I mean that like many compressors out there, it compresses the band above some settable threshold. For example 3:1 compression means that for every 3 dB above threshold of input signal, the output increases only by 1 dB. Generally, such compressors need make-up gain to bring the signal level back up. The Opal does not do this. Instead, the gain adjustment on the unit boosts the entire signal, not just the bandpass compressed portion.

The Kyma Compressors, on the other hand work without needing makeup gain in the traditional sense. You can think of them as compressing by the ratio starting at 0 dBFS. For every decrease of 3 dB on the input signal, the Kyma compressors drop the output by only 1 dB. Then to give some headroom SSI applies -10 dB of postgain to the compressed output. But aside from that attenuation, the Kyma compressors would never need any kind of boost on the compressed signal to bring their levels back up. Just the opposite of many analog style compressors out there.

So my Compressive EQ is simply a Kyma implementation of the BSS Opal, without its failures for postgain...

-- DavidMcClain - 17 Feb 2004

Hi David, I really don't care that much about the coloration at high frequency... knowing that from 8k to 12.5k my hearing graph drop by about 40 db, if I remenber correctly. That brings me to another question; you find 92k and 192k attractive. I can understand that ideally the sampling rate should be as high as possible because of high freq harmonic differentials etc.... But praticaly, it looks like the higher the sampling rate is, the less sound quality improve. I mean, from 11k to 22k it's like a giant step but from 48k to 100k I don't find the difference worth the price. Since multiplying sample rate by 2 actually means multiplying processor load by MORE than 2 I tend to stay at lower sample rate. i.e. I don't find 96k sound as twice as good as 48k. I prefer to have four 48k channel rather than one 192k... As a DSP programmer what do you think about high res efficacy?

-- KarlMousseau - 17 Feb 2004

This is a fantastic EQ, it is not a transparent EQ, it changes the graph from 7 k upwards, which is noticeable when you bypass compare , but the bass end response makes it fantastic for mastering applications , in my opinion, even though though the sound is being coloured just by going through the filterbank... I have been getting some exciting results with various material...

Be aware that David's stereo versions both have a fault in the channel seperations at the start of the chain - the RightChannelOnly? has both right and left ticked - Later tonight I will post a corrected and customised version of the stereo version ... I have also connected the top hpf to the full bandwidth source instead of the last butterworth band ... this gives the expected twinkle on the 16k slider ...

-- CristianVogel - 25 Jul 2006

Thanks Cristian for an update on this great sound! I found the treble coloration less noticeable when the 16k fader was turned down a dozen dB. I suggest to remove the ForcedProcessorAssignment? prototype to let the scheduler do a better job.

-- CamilleTroillard - 06 Sep 2006