why does decreasing EQ increase the main meter level?

I have a stereo WAV file that I wanted to decrease the very low end. I input the file into Logic. The music is fairly compressed and peaks at -0.4 dB. When I apply ANY EQ plugin in Logic and decrease the low end, the track meter levels go UP and into the red (the same thing happens in Waveburner). This makes absolutely no sense to me. The only effect I am applying to the track is EQ. Faders are at zero. In addition to going into the red, the track meter behaves as if the sound is less compressed (i.e. it bounces around more). Although it goes into the red, I do not hear any noticeable distortion. (On the other hand, if I use the EQ to increase the low end, it goes into the red and I hear the distortion, as expected) If I bounce the track while applying the EQ, the resulting file peaks at 0 dB (i.e. higher than the original track). What is going on? Are the meters just not accurate?

That's nothing surprising. EQing and dynamic are related. Just as compressing changes the frequency content of the original material, EQing changes the level of the original material.

 

Take a square wave, and filter off the high frequencies, your peak level will go up since you're rounding off the edges.

 

I wish I could draw it for you... do you understand?

I don't understand. I understand why EQ-ing will change the level, but why is not as straight forward as turning EQ down means overall level goes down. I am subtracting dBs in a certain frequency range. Where does the increase in dB in the overall mix come from? How can both decreasing and increasing an EQ in acertain frequency range BOTH increase the overall level? Why shouldn't I just view the EQ-ing as decreasing the level of a certain range of frequencies and the overall level being the sum of all the levels of all the frequencies (or some integral of dBs overall frequencies)? Does it have to do with certain frequencies interfering with each other and cancelling out and by removing certain frequencies things are no longer cancelling out?

I'm curious about this myself. It seems counterintuitive to expect level to go up when you're decreasing the overall energy in the audio spectrum.

 

Re rounding off the edges of a square wave, say you're doing this using a standard lowpass filter in a synth, with resonance set to zero. I can't say that I've ever seen a situation where the level would increase as a result. The only exception I can think of is if the filter wasn't being modulated by keyboard tracking, a boost in level (actual or perceived) might occur if the frequency of the fundamental (or first harmonic) approached or matched the cutoff frequency of the filter. Still, the filter would have to have a fairly resonant quality for this to happen.

 

So like I said, I'm curious about this also. Any add'l explanations?

Assuming you're not applying any post-EQ compression, the only reasons I can think of are:

 

• The summing engine is auto-adaptive, i.e. float, and it takes 0dB as a reference for maximum levels.

 

• Or the EQ is flawed - and like some real-world analogue circuits, there is slight resonance arount the selected frequency.

No, it's pure math, and has nothing to do with digital vs analog, or even less to do with Logic's way to deal with digital audio.

 

Again, pure math: take a square signal and filter the high frequency components, and you will end up with a resulting signal that peaks higher (even though it has less energy).

 

I'll try to find more time (maybe later tonight) to go into this a little more.

 

PS: I agree it can seem counterintuitive!

 

Re rounding off the edges of a square wave, say you're doing this using a standard lowpass filter in a synth, with resonance set to zero. I can't say that I've ever seen a situation where the level would increase as a result.

RMS level goes down, peak level goes up.

No, it's pure math, and has nothing to do with digital vs analog, or even less to do with Logic's way to deal with digital audio.

 

Again, pure math: take a square signal and filter the high frequency components, and you will end up with a resulting signal that peaks higher (even though it has less energy).

 

I've really scratched my head over this one, but I don't get it.

 

I can accept that a fiiltered square wave can have a higher peak level than a pure® square wave, given both have the same rms level, but I fail to see how filtering can per se increase the peaks . . . please enlighten . . .

OK. A picture speaks a thousand words, so here's what I did:

 

1) I took an ES 2 and generated a simple square wave with it. In a perfect, theoretical world, this square wave would contain harmonies that go up to an infinite frequency and the wave is perfectly square: perfect vertical lines and horizontal lines. In the real world, there is no such thing as a perfect square wave, and the harmonies are limited by the generators, and in this case, the nyquist frequency since we're working in digital.

 

2) I bounced that square wave dry first, then through a Channel EQ featuring a single lowpass, Q = 0.71 (no resonance), slope = 48dB/octave, frequency = 15KHz.

 

3) I look at my meters on the Audio Instrument channel strip: When the Channel EQ is off, my square wave peaks at -8.9dBFS. With the EQ on, my filtered square wave peaks at -7.4dBFS (higher).

 

4) I open both bounced files in a sample editor: You can clearly see that while the unfiltered square wave (left) peaks at around 30% (an in theory, if it was a perfect square, it would actually peak somewhere around 28%). However, the filtered square (on the right), peaks at around 43%. You can clearly see how filtering high frequency content alters the shape of the waveform, and, in this case, raises the maximum level of the waveform (peak level of the signal).

 

One interesting application of this phenomenon was used by two TC Electronic engineers in a whitepaper claiming that any CD mastered above -3dBFS might distort lesser quality converters found in consumer electronics: you make sure you master at -0.1dBFS (peak), yet that digital signal actually represents an analog signal that would peak at +2.5dBFS, once filtered by the 22KHz lowpass found in such converters.

 

To go a little further: let's say you have A/D converters that are calibrated to convert a maximum analog signal of 5V (peak) into 0dBFS. You then tweak the audio in Logic, and master at 0dB peak. Without realizing it, you are most probably generating a signal that is a digital representation of an analog signal that peaks above 5V. Your converter might not be able to produce that signal, hence the distortion. In fact, your converter might be able to produce that signal, but not Joe Schmoe's boombox's converters! That's when you're in trouble.

 

Obviously, nobody cares, and everybody is more interested in getting a HOT signal than avoiding unnecessary distortion.

Edited September 18, 2006 by David Nahmani

So the moral of the story is not to use process square waves with TC gear.

 

 

On a more serious note, that's mighty interesting stuff. I appreciate the time and trouble you went through post that explanation David.

 

Best,

 

-=sKi=-

You can also do a simple test with white noise (wich contains all frequencies): insert a Test Oscillator plug-in on an Audio Instrument object and set it to white noise so that the level on your master Out 1-2 is at -3dBFS. Insert a single Channel EQ plug-in on that Out 1-2 object and set it to lowpass, cutoff = 20KHz, Slope = 48dB/Oct, Q = 0.71. Your master should overload at around +3dBFS.

David, I'd be interested to read that white paper.

 

My understanding - which is always open to revision - as to why 0dB peaks can lead to clipping in D/A converters was that two digital values at 0dB (for example) can describe a sine wave which upon reconstruction is >0dB . . . ?

 

Also, I cannot (and do not) dispute your findings re squares and peaks (sounds like an album title, Micheal . . . ) but I remain unhappy with the any technical explanation I can muster . . .

 

Surely, if you take a square wave and progressively filter it to its fundamental frequency, you end up with a sine wave? If the peak values of these are different - which would seem unlikely to me, but may be - this might offer an explanation.

 

I'm still prefereing the possibility that this is a characteristic (flaw) in the EQ being used, and I guess the thing would be for me to try the same procedure with different EQ/filters . . .

Yes, you can try the same experiment with any EQ and will find the same result. It is not a fault in the EQ.

 

Here's a link to the paper I mentioned (pdf): 0dBFS+ Levels in Digital Mastering

 

My understanding - which is always open to revision - as to why 0dB peaks can lead to clipping in D/A converters was that two digital values at 0dB (for example) can describe a sine wave which upon reconstruction is >0dB . . . ?

Yes, which is exactly what I was trying to describe. This is due to the lowpass filtering that happens in the D/A converters. Same thing happens when filtering a square wave.

David,

 

Sorry to re-hash this subject, but despite your post on this subject I still can't get my head around the difference between the math as I've always understood it and the actual operation of the EQ (or of a filter) in Logic and how it affects overall level...

 

The following graphs were made using the cool and ever-geeky Apple Grapher utility. In the first pic I'm showing a waveform created by simple additivie synthesis forming the equivalent of a filtered sawtooth wave (fundamental plus first four harmonics). Note the peak level of the waveform. In the second pic I removed all of the partials, leaving just the fundamental (sine wave). Note that the peak level is lower, not higher, and this is what I'd expect, i.e., anytime you remove (filter) partials/harmonics from a waveform the overall energy (amplitude) of that waveform must be lower. However, that's not what you showed in your waveform diagrams, hence my confusion.

 

I'm also aware that even digital EQ has a 'color' to it and may not produce mathematically perfect modifications to an audio file. But the whole idea of subtracting energy from an audio file, whether it's via a filter or EQ, and to have the peak level increase as a result just doesn't seem to make sense from a mathematical point of view. Could be wrong tho...

http://www.soundonsound.com/forum/showflat.php?Cat=&Board=MRT&Number=267877&Searchpage=2&Main=267316&Words=high+pass+filter&topic=&Search=true#Post267877

Ah, phase shift. That explains a lot. Thanks mik.

the whole idea of subtracting energy from an audio file, whether it's via a filter or EQ, and to have the peak level increase as a result just doesn't seem to make sense from a mathematical point of view.

I don't see why? You can easily create a signal that has a very high peak level and almost no energy (impulse). Inversely, you can easily create a signal that has a low peak level and high energy (square wave). Peak level and energy are not related in any way (unless you're comparing two waveforms that have the exact same shape).

 

It would be interesting if you could try your test with a square wave?

Ah, phase shift. That explains a lot. Thanks mik.

That's not the explanation, and I'm sorry to say but the SOS poster is wrong: you can easily use a linear phase EQ to raise the peak level by +4dB when cutting high frequencies.

Edited September 24, 2006 by David Nahmani

Ski, the animated picture below should explain better what I'm trying to explain. You can see that as you add the square wave harmonics to a sine wave, it slowly comes closer to being a perfect square wave with a lower amplitude (hence the lower peak level).

 

Nothing to do with phase shifting.

 

On the picture below, take the square wave and filter its harmonics, and you'll end up with the sine wave, which has a higher peak level. That's what you experience when you cut frequencies with an EQ and see the peak level rise.

 

http://upload.wikimedia.org/wikipedia/commons/0/0a/Synthesis_square.gif

 

Source: http://en.wikipedia.org/wiki/Square_wave

Wow, took me what, forever to reply?!?

 

Indeed, we saw this behavior together on my analog 'scope when I gave the analog synth seminar last month. (Digitally) filtering a square wave resulted in an increase in amplitude at a certain point during the filtering.

 

It occurs, it's real.

Indeed, we saw this behavior together on my analog 'scope when I gave the analog synth seminar last month. (Digitally) filtering a square wave resulted in an increase in amplitude at a certain point during the filtering.

 

We sure did! Thanks for updating the thread. It's kinda fun starting a thread about mathematical and theoretical arguments, and ending up plugging Logic into the scope and actually see the results on a graphic display. I'm glad we did this! Plus I don't usually have an oscilloscope lying around...

that's so funny......had no idea this post was so old when i started....

At least nw users (like me) have the benefit of reading these informative posts.

 

Old but still gold

f'sho

Nice graphs here! I think square waves are best suited to show what's going on. The little animation above shows how the peak level decreases as the amount of summed harmonics increases.

May I at this point redirect to a newer thread with some oscilloscope screen shots from a very basic experiment with real electronic components: http://www.logicprohelp.com/forum/viewtopic.php?t=20074