Last week I wrote about the phase issues that might become a problem when you're using pass filters, specifically high-pass filters. This week, we're looking at the digital side of that, and we'll figure out the differences between minimum-phase and linear-phase filters.

One sentence recap: hi-pass filters can cause audible phase shift issues at frequencies near the cutoff frequency and their overtones.

All of this phase issue stuff is baked into the physics of sound, and it is all because frequency happens over time.

Ears, Analog and Digital

Think about a bell. You hear a bell, and you don't know the pitch of the bell until the resonance of the bell develops and your ear recognizes that. The clangs of different-pitched bells essentially all sound the same. And the same is true for drums. The attack of a drum doesn't tell you its pitch, but its sustain and resonance do.

Here’s a visual representation. If I show you just a sliver of the frequency response graph, you don't know how this sounds. If I show you more, you get more information and the sound of things becomes more apparent.

The only way your ear can recognize more frequencies is to spend more time listening.

In practice, your ear needs to hear at least a cycle of a waveform, and usually more than one cycle, to decide what a sound “is,” what frequencies it contains. Your ear needs about 20ms on average to “know” a sound. However, this time varies due to frequency. Your ear figures out high frequencies faster than low frequencies, because high frequencies cycle faster, your ear gets more information in a shorter amount of time. This is a REALLY IMPORTANT CONCEPT. If you get this, you’ll understand the rest.

An analog filter circuit doesn’t figure out what a frequency is like your ear does. And it doesn’t respond to all frequencies the same way. Analog filters use capacitors and inductors to modify frequency response, and the way these work is that the energy of a signal is stored in an electric or magnetic field. That stored energy can pass or hamper a signal depending on its frequency, as it moves through the circuit, and that's what gives us the response curve. Higher frequencies tend to get through the circuit faster than lower frequencies. If one frequency gets through faster than another, there is a time delay difference between them. These are very short time delays — too short to manifest as a discrete delay like an echo. Instead, as with all very short time delays, we hear them as phase shift. So a signal passing through analog processing, like a pass filter, comes out with a range of phase shifts across its frequencies.

This range of phase shifts is referred to as Group Delay, so if you see that term, that’s what it’s referring to, the phase response curve of a bunch of frequencies—a group.

Let's equate some concepts here to help you understand all this: your ear taking time to figure out the frequency is like an analog circuit passing through some frequencies slower than others. Time and Frequency are tightly knit together.

NOW... digital processing... you’d think that a digital processor could be programmed like, “lower 200Hz by 2dB,” and it could do that without any phase issues, just like you can tell a digital processor, “Lower the gain of this entire signal by 2dB” by sliding the fader down. But a digital processor can’t single out a frequency so easily, because, like your ear, a digital processor needs time to recognize a frequency.

At any sample point of a digital signal, all there is is a voltage, a number that has no sound or frequency to it. To recognize a sound, a digital processor needs multiple numbers across time; again, this is very much like your ear. And like your ear, it figures out higher frequencies faster than lower frequencies. So, if you feed a signal through a digital processor, and that processor has a response curve to it with different frequencies at different amplitudes, it processes the frequencies as soon as it recognizes them, but it recognizes the higher frequencies quicker than the lower frequencies... and again, the frequencies are phase shifted, just like in our analog example.

Another thought here: any sample point in a digital signal is a number. It is very easy to add, subtract, multiply, divide or do math to that single number. That is what GAIN, or moving a fader, does: math to those numbers. But a digital processor, to affect frequency, needs a bunch of numbers to figure out the frequencies in the first place, and getting those numbers and doing yet more math takes time.

Again, let’s equate the concepts here: your ear taking time to figure out the frequency is like an analog circuit passing through some frequencies slower than others is like a digital processor needing time to calculate a frequency and then process it, and it does this faster or slower, depending on the frequency. Again, time and frequency are tightly knit together.

You’ve probably heard of Minimal-Phase and Linear-Phase filters and Equalizers. Maybe you’ve wondered about the differences. You didn’t? Well, tough, we’ll cover it here anyway. This week: Minimal-Phase; Next week: Linear-Phase.

Minimal-Phase Filtering

A digital Minimal-Phase filter or EQ essentially has the same phase response as the same sort of analog filter or EQ. With both of them, the largest amount of phase shift is located around the cutoff frequency. The digital circuit causes phase shifts in this area, and this is the minimal amount of phase shift needed to do the job. Hence Minimal-Phase.

The better question is, why is the largest amount of phase shift around the cutoff frequency?

Because at the cutoff frequency, the filter goes from doing nothing special—passing signal through—to suddenly having to do work—reduce the amplitude of certain frequencies. The phase changes at that point, and this is the same for an analog circuit.

Now, let’s look at the slope of the filter. If we have a shallow slope, it becomes intuitive that both the analog and the digital filters can first respond to the high frequencies, and then sort of work their way down to the lower frequencies a little bit later.

But if the slope is steep, then there is more information to work through in less time, there is a lag, and the phase issues increase.

If the circuit is processing simple information, like a signal with a limited bandwidth, or a signal that is mainly low-end or high-end, it is relatively easy for either an analog or digital circuit to do its job.

What if we cram a whole bunch of frequency information into it in a very short period of time? Like the clang of a bell? Like a very fast transient?

The circuit has to work on a bunch of frequencies all at once, but it has limited capability to do that, so again, it does the high stuff quicker than the low stuff, causing phase issues. So yes, typically fast transients will exhibit more phase issues—the transient “smears” as the highs arrive earlier than the lows.

To really make this bad, slam a fast transient through a pass filter with a steep curve, and the circuit just doesn’t have time to properly respond. It needs more information which means it needs more time.

What does that janky response look like?

In an analog circuit, it sort of gets confused, and rather than letting the low frequencies through evenly, it does it in spurts, sort of like, “Uh, let these highs through Oh Oh oh! Need to let some lows through and Oh Oh Oh more highs and some midrange and Oh OH OH some more lows.” It oscillates. These oscillations happen mainly in the low frequencies, after the transient, and this is called Ringing.

Ringing

What does ringing sound like? First of all, because it is happening after the transient, it is somewhat masked by everything following the transient, so it usually isn’t much of an issue. Depending on the cutoff frequency—like if it's high, our ears might kinda like it. The transient hangs out a little longer or gains a bit of color. Lower frequency ringing can sound “boingy,” a low-frequency resonance for a moment. Depending on the slope and frequency, it can manifest as a pitchy wobble. All of this is very hard to hear. You might sense, “This sounds off” way before you hear it as a low-frequency pitch wobble.

Digital circuits ring in a similar manner to the analog circuit. It processes the high stuff quickly, squirts out the low stuff after the transient has passed, with just about the same result in terms of effect on the sound.

This is a brainful. The key things to remember are that processing frequencies, whether in your brain or in an analog circuit or a digital algorithm, happen across time, and the speed of recognition/affect/processing is dependent on frequency. The timing difference between the different frequencies results in phase shifts across the signal, but they’re spread out—no shift at some frequencies and more at others as the frequency approaches the cutoff frequency. Ringing is a problem in circumstances where the circuit or processor lags enough that it releases some frequency information late compared to the entirety of the transient. This manifests as an oscillation. It’s hard to hear, and mostly noticed on fast transients with low cutoff frequencies.

Next week, we’ll look at Linear-Phase filtering.

When I was coming up through studios as a wee small lad with a big mouth, it was standard operating procedure to use high-pass filters all over the place to roll off the bottom end of things. There were high-pass filters on microphones and channel strips—sometimes just a button with a single roll-off at 75Hz, but sometimes it was variable. And we were always switching these things on.

And there appeared to be good reason to. High-passing a vocal mic got rid of the thumps and bumps of feet on the floor and mitigated, somewhat, the low-end buildup caused by proximity effect. Switching it in on guitars took out the subsonic mess, ditto on tom mics and overheads. And besides, THE FAMOUS GUYS were doing it, the guys who knew more than me and had decades of experience.

Now, the FAMOUS GUYS are saying NO!!! Never use high-pass filters! They cause all sorts of phase issues! Guys on audio forums light each other on fire over this issue.

(delivered in a whisper: frankly, I'm pretty sure most guys on forums freaking out over this can't hear the difference, but...)

What is the story here? Has something changed because we’re all digital now? And what is the Useful Truth of the Matter?

Phase and EQ

EQs work because of phase shift. You can think of an EQ as a phase shifter that affects frequency response. How to explain this in a simple way...

A low frequency, say 100 Hz, changes from a peak to a dip more slowly than a 1000Hz changes from a peak to a dip. As frequency goes up, there are more changes from peak to dip across time. Low frequencies change amplitude “less often” over time; high frequencies change “more often” over time.

If you feed that waveform into a circuit, that circuit has to work with the less often/more often, which means that a circuit might respond faster or slower, depending on the frequency. The result is some frequencies get delayed compared to others, and that causes different amounts of phase shift depending on the frequency.

Then, that signal with all the phase shifts gets mixed in with an unprocessed signal. Those shifts can cancel or boost, and that changes the frequency response. Frequencies with a lot of shift affect the amplitude at that frequency more. Now, there aren't literally two separate signal paths in the circuit, one unprocessed and the other phase shifted, but it does kind of work like that in the mysterious world of the electron, and it is useful to think of it like that, as a way of understanding it.

Paul Wolff would kick me under the table over this explanation. Sigh.

All EQs come with phase shift, but the amount depends on the type of EQ or filter.

Why is it especially an issue for high-pass filters?

Earlier, I mentioned a high-pass filter with a frequency of 75Hz. This is the cut-off frequency—the spot where the frequency response drops by 3dB, indicating that’s where the cutting occurs. The cut. It is at that point where the largest amount of phase shift happens. Maximum Phase Rotation. 75Hz is close to an open D string on a bass—the same note you get when you tune down the low E on a guitar to do a dropped D tuning. This is pretty low. The majority of notes and music in a song happen much higher.

But, what if you high-pass the bass down at 40Hz, roll off some of the low end of the guitars down there at 75Hz, and clean up the kick by high-passing it at 30Hz? Now you’ve got 3 areas of maximum phase rotation happening across a bandwidth of about an octave, from 30Hz to 75Hz. All those rotations combine and mix in a tiny and really critical area of the mix. You made all those cuts down there ostensibly to tighten up the low-end, but now it’s a mess, and it becomes murky and weak down there.

What happens if you start setting the cutoff frequencies higher? Well, then you're moving them into where more of the music is, into where vocals happen, etc. And then they can become more noticeable. A vocal high-passed at 120Hz, a guitar at 150Hz, a piano at 100Hz — now the phase rotation from each of those is happening in a range where there are fundamentals, harmonics, and formants all interacting. It's like dropping a phase bomb in the middle of the music party.

How does this sound? Is it extreme? Is it like when two mics on a guitar speaker are out of phase?

No. It's way more subtle than that. And on one instrument only, it’s unlikely you’ll hear it. But when you mix together a bunch of sources with high-passing, you'll start noticing a thinning or a very slight hollowness. I tend to notice it in situations where I have a bunch of channels up, and then I bring up more, and instead of getting "bigger," the whole thing seems to get smaller. Or something gets weird somewhere. A sound loses presence or clarity or... just dies a little.

The slope of a pass filter exacerbates it. The slope is how many dBs of attenuation happen per octave. A shallow 6dB per octave slope has much less rotation than a steep 24dB per octave slope, which has tons.

Been using those steep slopes in the bottom end, haven't ya?

Fixing the problem

Nothing is a problem if you like how it sounds. Or if the client likes how it sounds and pays you. I've never heard anyone hum a lack of phase shift or % harmonic distortion. You can get very anal over this stuff.

But let's not be idiots and shitty engineers. Here are some guidelines.

1) Try to avoid steep slopes on pass filters.

2) If you can adjust the frequency of the cutoff, don't set it to something in the middle of the music or where a majority of the notes are clustered. Go lower with a high-pass, or higher with a low-pass.

3) If the lowest note of a part is around 110Hz, set the cutoff at least a half octave below that. So, around 70Hz in this case. That way, the maximum phase rotation is comfortably below the lowest note.

4) Don't use multiple high-pass filters on a track. If you're going to use one, then use ONE.

5) If you have to high-pass a bunch of tracks that are all in a similar frequency area, spread the cutoff frequencies out. One at 30Hz, another at 100Hz and one at 70Hz still sucks, but it's better than everybody at 70Hz.

6) Got a bunch of guitars with a lot of low-end buildup? Don't individually filter them: bus them together and then filter the bus.

7) Use shelves instead of pass-filters to clean up things in the mix. They have less phase shift. In general, the broader and more gentle the action of the filter or EQ, the less the phase issues. A wide Q (bandwidth) parametric setting has less phase rotation than a tight Q parametric setting.

8) Back to the low end: think like, "I'm going to high-pass the bass, use a parametric to boost up what I want in the kick—so like a boost at 30Hz and another 2kHz to get the thump and the click, and then run the kick lower in the mix, and use a low shelf cut to clean up the guitars down there."

9) Remember, the phase issues compound as you add things to the mix, and I mean not only adding channels and tracks, but EQ and effects as well.

10) The more you think about this stuff, the more you'll think you can hear it, the more you'll drive yourself crazy, the less people will like you. Don't die alone over high-pass filters.

Low-pass filtering

Low-pass filters (which roll off the highs) also cause audible phase anomalies, but it is generally less of a concern. First of all, the tendency is to use high shelves up there rather than pass filters, and shelves cause less issues. Secondly, while there is critical information up there, there aren’t a lot of fundamentals and first harmonics up there, so the effect isn’t as musically detrimental. Now, if you’re doing a lot of pass cuts in the 4kHz to 8kHz, that can definitely cause audible issues and interfere with clarity and definition, but how often does that happen? Never?

Most of our plug-ins have pass filters on them. You can think of them as corrective tools for fixing issues. Our Shure Level-Loc has pass filters on both the input and output. These are better thought of as creative tools, and remember, we have them there at the suggestion of Tchad Blake, who is one of the most creative guys out there.

We’ll be covering more on tech side of filters and equalization in the next few weeks.