What is the relation between high pass (low cut) filters and headroom?

Question

I use, just like most of you I guess, high pass filters in my mixdowns to clean up muddyness and save headroom. I have a subscription on Computer Music in which every month a producer named Owen The Geek tries to bust myths or explain very advanced mixing tricks and tips.

A few months ago he took the myth of saving headroom by filtering out the sub bass frequencies. he started at 20hz and moved his way up to show the way headroom was affected.

He used different waveforms that you would find on any subtractive synth.(sine, square,triangle and a saw)

A sine wave increased slightly in headroom when applying the filter. incresing even more if the cutoff was raised.

But the other 3 waveforms decreased in headroom with the filter applied. They raised even more with the cutoff raising until they started dropping (between 500hz and 1khz)

Why is this happening? should I change the way I use a high pass? How will this affect complex lead sounds that I use to produce my music?

EDTI: I would love to show you the video he made as a prove but it's copyrighted so I can't upload it to youtube

Answer 1

Side note: BRHSM (OP) is refering to Geek Technique #12 in issue 222 of Computer Music magazine.

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Great question, BRHSM. I have three answers for you, but only one is true. I'll let you come to your own conclusions. :)

Option 1: I must confess, the video is one big deception.

Everyone knows that filters always reduce amplitude and increase available headroom, without exception.

Weeks of planning and editing went into conjuring the illusion that high pass filters often cause an increase in amplitude.

I did it so that I could provide false evidence in arguments against people who I secretly agree with - and I would've gotten away with it if it weren't for you meddling kids!

Option 2: I made a foolish mistake. Steinberg and iZotope's software misrepresents waveforms, frequency spectrums, filter curves, and amplitude meters - everyone knew this except for me.

Also, the staff at Computer Music have no common sense. They add fools to their experts roster and print wild assertions without fact checking.

Option 3: The video is accompanied by a 2-page article, which includes ~600 words of info that's not in the video to help you make sense of it all. There's also an email address so you're welcome to send your questions to me directly. :)

The point of the piece wasn't to discredit all uses of high pass filters. I specifically oppose the habit of blindly highpassing, hoping to save headroom, without checking before/after for tonal shifts and any unwanted increase in headroom.

The myth is that filtering always reduces amplitude - it doesn't. I showed that it doesn't using test signals, then I showed that it doesn't using musical signals.

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Anyway, you asked why this is happening. You might want to review the video, but basically a complex waveform is made from multiple frequencies - sines. If you alter the amplitude and/or phase relationship between those frequencies, the waveform will change accordingly.

It's not an easy concept to explain clearly in words, which is exactly why we made the video. One way to think of it is to imagine that some of the frequencies are being 'clamped down' by some of the other frequencies - so reducing certain frequencies may reduce the 'clamping effect', thus resulting in an increase of total amplitude.

You also asked how this will affect complex lead sounds. Again, I'd ask you to refer to the article, but for the sake of giving a complete answer; it'll probably make them take up more headroom, it may even have a negative impact on the timbre as well.

By the way, Michael Hansen Buur's fantastic answer raises the important distinction between traditional mic'd sound sources and virtual synths. I didn't get into that in my article, but in any case here's what you should do:

1) Measure the amplitude

2) Add your high pass

3) Measure the amplitude again

4) Make your decision

It really is that simple. The point of the piece was that we should all engage in critical thinking instead of blindly doing what everyone says we should do. Just don't apply the filter unless you're satisfied it's doing what you want it to do and nothing else.

By the way, if you're into making modern/electronic music, there's an email course on making mixdowns easy starting at the end of the month, totally free to join. Head over to www.owenthegeek.com and enter your email address.

Best,

Owen...

Answer 2

The idea of using high passes for the exact reasons you mention is spot on ("clean up muddyness and save headroom"):

Regarding "muddyness": If the microphone is placed closed to the source, it may pick up more low frequency energy than we usually associate with the sound of that source (vibrating floor toms and breath are a good examples). The microphone characteristics, room acoustics and bleeding from other sources (mostly relevant in live sound) may also result in more lows than wanted. High Pass / Low Cut filters can really help out here.

Regarding "headroom": To really understand why high pass filters are mentioned in relation to headroom, think about how a direct current (DC) signal works for a second:

If we hook up a small battery to a speaker (which of course you wouldn't do, right!?), it will push the membrane to a fixed position (pull or push depending on the polarity). If we then also hooked up our audio signal to that speaker (along with the battery), we'd hear something, but it would lack dynamics and low frequencies, because the membrane is being constantly held at a position and in relation to our audio signal this new position becomes the zero crossing point. If you ever tried touching/holding the membrane of a speaker you'll know what I mean too.

Now back to the audio signals: some signals actually contain a DC offset (and thats really bad). Typically caused by bad/broken mics, DI's or interfaces. Using a high pass will remove that, as we can think of DC signals as an infinitely low frequency (which is really nonsense, but that is how it works anyway). In the analog world, the capacitor involved in the High Pass circuit is the one that blocks the DC signal.

But even without real DC offsets we can still have unwanted low frequencies that momentarily "move" the zero crossing point (rumble, hums, too deep bass, kicks and toms etc). So with the battery-example in mind it easy to understand how such stuff - albeit momentarily - affect the headroom of the wanted signals.

So I'd say you should have a really good reason not to use high passes (like kicks, basses and deep virtual synths). Always use them, except when they kill some of that wanted stuff, and use them on individual channels, not on the master bus, unless you set it really low (10-15 Hz or so). Here you should use a DC removal step instead, like available in Voxengo Elephant, so you don't loose intended lows.

Regarding that test by Owen The Geek and the increase in volume: From what you describe, I think he misses the point about why and when to use high passes. It is about reducing reducing the low end energy (which often contain unwanted material). In general taking out energy means more headroom for higher frequencies.

Yes it may amplify the peak, that is just how some filters work (the nature of second-order filters, different Q settings and approximity of the program material to the cutoff/center frequency). Filters resonate and amplify certain harmonies. Phaseshifting may also take place, which may take part in the increased peak amplitude (source).

Answer 3

Using an HPF on a sine wave will reduce the amplitude of the signal as the filter gets closer to that frequency. And the same thing happens with other waveforms - only they will have harmonics as well. So the filter should not be amplifying the signal at all.

I think what is key here is the shape of the filter: as you describe it, it must have a slight increase before the cutoff "knee" - useful information on the shape (and equations) for filters here.

Answer 4

As long as a filter is removing harmonic content from a signal, the headroom will increase accordingly. With a high-pass filter, the low frequency energy of a signal can be removed more directly.

In music production this is the filter that would dampen the bulk energy of the song. When removed, the sub, bass and muddy frequencies would then offer a lot of headroom.

On the contrary, to make up for the same amount loss of headroom with the higher frequencies, you could create a very bright and loud track. However, the spectrum would be imbalanced and fatiguing.

When using synths - you will indeed have more headroom by using a high-pass filter (especially on low pitches), or possibly by using high pitched notes. Synths may have their own post-processing applied to alter the output depending on pitch, which can be modified with Key Tracking or Key Scaling.

I know that in NI Absynth, Wavetables themselves contain a sum of 512 harmonics, and when some harmonics are removed or filtered out, the waveform Amplitude (and shape) directly corresponds. I.e. Although using a Lowpass filter will make a Sawtooth less bright and slightly quieter, the High-pass filter will dramatically alter the headroom, since the lowest frequency of the wave period is the fundamental frequency (of the used pitch).

A great visual is this part of a video on Additive synthesis; it shows how a Saw wave is constructed with many harmonics, the lowest ones having the highest amplitude.

The Fractalize Absynth video of mine also demonstrates this happening in both directions of amplitude - adding high multiple harmonics (Fractalize) to a waveform will reduce the fundamental harmonic(s) to maintain the same headroom on the wavetable, while removing lower harmonics will rapidly reduce the amplitude.