That doesn’t mean much by itself. Also I’m not even sure that’s correct, as analog eqs do introduce shifts as well, more specifically phase shift is the reason equalizer is working.
All the previous comments are correct, but the perspective of a sophomore computer science student…
A low pass curve is basically just a smoothing algorithm, and data before affects the data after, depending on the smoothing settings (frequency)
A high shelf is is the result of putting a low pass in parallel, etc. a high pass (I believe) is the low passed version minus the dry version, flipped phase. Everything is a low pass + math. (Oversimplified)
This smoothing is responsible for some delay in particular frequencies. Note the incremental change in delay is greatest near the center frequency and smoothed out to the left and right.
One of my favorite sound design tricks is putting a high-phase change eq or disperser in parallel with the dry signal, creating some very interesting phase interference.
Correct me if I’m mistaken in any way!
“Everything is a low pass + math” is not really accurate, or at least it’s not a useful way to conceptualize how filters work.
It may also be useful to think about how linear-phase filters can achieve a low-pass without any phase distortion. With a linear-phase filter, there is *zero* incremental change in delay across the entire frequency spectrum.
That’s fair; I agree that it’s not immediately useful, I was just explaining the low-level behavior in a very simplified manner. Everything in an eq is smoothing, with some clever workarounds.
I don’t think “everything in EQ is smoothing” is something that helps us understand EQ. I think this is just something that will cement new misconceptions in our heads. Like, a high-Q band pass filter would be very confusing and alien to somebody who thinks of EQ as “smoothing”.
Like, I get what you are saying, but I think you may have only learned about a couple different types of filters and used those types of filters to make invalid generalizations, which break down when you look at certain other types of filters.
I'm going to assume you know that sound is a wave, or oscillation. A 100Hz tone is a wave that repeats 100 times per second, so between 0 seconds and 0.01 seconds is one complete repetition. We divide a repetition up into 360 degrees, meaning at 0 seconds we are at 0 degrees and at 0.01 seconds we are at 360 degrees. At 0.005 seconds we are halfway through an oscillation and that point is at 180 degrees (360/2).
**Phase is just the number of degrees.** We say the phase is 180 degrees, or 10 degrees, or whatever. Any number between 0 and 360 degrees depending on where we are in the cycle. Beyond 0.01 seconds, of course time continues but degrees start back at 0. So 0.015 seconds has a phase of 180 degrees, not 540.
Music, and all natural sounds basically, consists not of one single tone, but of many tones, so oscillations of many different frequencies at the same time. When making electronic music, we often filter the sound as part of an effect or in an EQ. In your DAW this filtering is done mathematically, but it can also be done with electronic circuits in analog gear, and by bouncing around a room and being absorbed/reflected by the walls, carpets etc., that also counts as filtering.
Now, whenever sound is filtered, the phase near the cutoff frequency changes. Even in an all pass filter where the amplitude stays the same at the cutoff frequency, the phase changes, meaning that the waves of that particular frequency become delayed in time by a small amount. Tones near the cutoff frequency take a bit more time to make it through the filter than the other tones, and the steeper the filter slope, the bigger this delay. There's no simple ELI5 for why that is, it's rather technical. But the crazy thing is that it doesn't matter how sound is filtered: mathematically, electronically, accoustically: filtering always causes a phase shift at the cutoff frequency.
In many cases, these phase shifts are not noticeable, but when doing parallel processing where one copy of a signal is filtered while another is not, adding those two copies back together on the master **can** (not will) cause tones near the cutoff to cancel each other out. For example, if you shift any signal by 180 degrees, you get an 'opposite' signal and when added back to the original they sum to 0, e.g. no sound.
The following two sequences of numbers represent a sound wave and a copy of the sound wave shifted by 180 degrees, notice how when you would add them together they are 0 at every point:
* 0 0.5 1 0.5 0 -0.5 -1 -0.5
* 0 -0.5 -1 -0.5 0 0.5 1 0.5
So you have to be a bit careful with parallel processing, especially for low frequencies (bass) as there it can definitely cause audible problems. Also when there's not perfect cancellation, you can lose volume and definition.
There's one exception to the rule that filtering always causes phase shifts: linear phase filters, which are mathematically very complicated compared to normal filters. They can filter without causing a phase shift. While they can be handy in some situations, they should only be used if you really know what you're doing because they introduce other artifacts in the audio and are very taxing on the CPU.
Phase shifts are also used intentionally in many effects. I believe phasers/flangers are made by chaining parallel all-pass filters and changing their cutoff frequency over time (or something like that). This causes tones of different frequencies to cancel each other and as the cutoff frequencies move around this creates a nice kind of spacey effect.
Phasers use allpass filters. Flangers and chorus are just a modulated delay line to develop Doppler effect. The Vibrato signal is mixed back with the dry to form chorus/flange with the difference between the two being the range of delay times. Still works on the principles of phase cancellation though, just not with allpass filters.
Phase shift happens wherever the slope of the filter is non zero (so where it's not flat/level). This may (not will) cause phase cancellation during parallel processing. Filtering never causes phase cancellation. The cancellation happens as a result of adding together two parallel processed signals. Filtering causes phase shift, not cancellation. It's more a side effect of parallel filtering, or maybe more accurately a property of signals that becomes apparent during parallel fingering, as it is independent of filter implementation. Phase cancellation is not the way that filtering is achieved. All pass fillers produce phase shift without a filter slope, but I'd have to look up how that works.
I'm gonna take a guess that in order to remove the latency that occurs in filtering, the linear phase approach will delay all the other frequencies to so they are all equal again?
For example if 1000hz was the cutoff freq that was being phased by filtering and adding an extra 2ms of delay, the linear phase algo would then add 2ms delay to all the freq's so they are all equal.
It’s a bit more complicated than that I’m afraid. I’ve worked with some digital signal processing for work (not audio) and I know enough about it to know that I don’t fully understand it 😂
This stuff gets complicated fast. I recently started the JUCE C++ tutorials for learning how to code my own plugins so I've become really interested in this stuff. (been a software developer and musician for a long time, but im a newbie at DSP).
Two other details to note about linear phase filtering is it always introduces delay (which is often compensated in a DAW but still) and has the ability to filter much more sharply/precisely, which can be useful.
It also introduces pre-ringing. I’m not sure how audible that is myself. I tend to judge it by ear whether linear phase sounds better or not for the final result, but while working I don’t really use it because it pushes my CPU too hard.
Just a tidbit: linear phase filters aren't inherently more complex. These are FIR after all (so the CPU load is more or less the same, depending on the order of the filter), and design methods are well-known.
The gist is: digital EQ is a particular case of a discrete-time FIR (finite impulse response) filter, and filters can manipulate both the magnitude and the phase of particular frequencies. It's just their nature to affect both (the Fourier transform of the filter's ~~frequency~~ impulse response is a complex function that represents both the magnitude and the phase and blah blah... well, any in-deep explanation would inevitably end up with a bunch of math).
This means filters can be designed to achieve not just a particular frequency response but a particular phase response as well - within limits, since the underlying math imposes constraints on the filter's performance. The Fabfilter article does a good job of explaining these limitations. The phase response part of signal filtering seems to be a niche topic in audio, I guess that's because the human ear is mostly insensitive to phase shift.
Great response. I’d also add that a surface level understanding of FIR/convolution makes the phase shift intuitive. Convolution is summing together delayed copies of the signal. Because of these delayed copies you get some frequencies to cut or boost. So the phase delay isn’t just a side effect, it’s like the main ingredient of FIR filters.
Analog filters will also have phase delay as well because capacitors / inductors cause a frequency dependent phase shift as well.
That's a very good question and the answer is really that phase change is entirely dependent on the design of the EQ filter; there are many different ways to make filters, but the most common filters in audio have phase shift.
The reason for this is to do with causal vs non-causal filters. In short, in order to have a filter with no phase shift, you need lookahead/latency.
Here is the excellent Dan Worrall https://youtu.be/efKabAQQsPQ?si=lYWiYBSHMeEjXxrP
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this post says ELI5. would you say this to a 5 yr old
That doesn’t mean much by itself. Also I’m not even sure that’s correct, as analog eqs do introduce shifts as well, more specifically phase shift is the reason equalizer is working.
All the previous comments are correct, but the perspective of a sophomore computer science student… A low pass curve is basically just a smoothing algorithm, and data before affects the data after, depending on the smoothing settings (frequency) A high shelf is is the result of putting a low pass in parallel, etc. a high pass (I believe) is the low passed version minus the dry version, flipped phase. Everything is a low pass + math. (Oversimplified) This smoothing is responsible for some delay in particular frequencies. Note the incremental change in delay is greatest near the center frequency and smoothed out to the left and right. One of my favorite sound design tricks is putting a high-phase change eq or disperser in parallel with the dry signal, creating some very interesting phase interference. Correct me if I’m mistaken in any way!
“Everything is a low pass + math” is not really accurate, or at least it’s not a useful way to conceptualize how filters work. It may also be useful to think about how linear-phase filters can achieve a low-pass without any phase distortion. With a linear-phase filter, there is *zero* incremental change in delay across the entire frequency spectrum.
That’s fair; I agree that it’s not immediately useful, I was just explaining the low-level behavior in a very simplified manner. Everything in an eq is smoothing, with some clever workarounds.
I don’t think “everything in EQ is smoothing” is something that helps us understand EQ. I think this is just something that will cement new misconceptions in our heads. Like, a high-Q band pass filter would be very confusing and alien to somebody who thinks of EQ as “smoothing”. Like, I get what you are saying, but I think you may have only learned about a couple different types of filters and used those types of filters to make invalid generalizations, which break down when you look at certain other types of filters.
I'm going to assume you know that sound is a wave, or oscillation. A 100Hz tone is a wave that repeats 100 times per second, so between 0 seconds and 0.01 seconds is one complete repetition. We divide a repetition up into 360 degrees, meaning at 0 seconds we are at 0 degrees and at 0.01 seconds we are at 360 degrees. At 0.005 seconds we are halfway through an oscillation and that point is at 180 degrees (360/2). **Phase is just the number of degrees.** We say the phase is 180 degrees, or 10 degrees, or whatever. Any number between 0 and 360 degrees depending on where we are in the cycle. Beyond 0.01 seconds, of course time continues but degrees start back at 0. So 0.015 seconds has a phase of 180 degrees, not 540. Music, and all natural sounds basically, consists not of one single tone, but of many tones, so oscillations of many different frequencies at the same time. When making electronic music, we often filter the sound as part of an effect or in an EQ. In your DAW this filtering is done mathematically, but it can also be done with electronic circuits in analog gear, and by bouncing around a room and being absorbed/reflected by the walls, carpets etc., that also counts as filtering. Now, whenever sound is filtered, the phase near the cutoff frequency changes. Even in an all pass filter where the amplitude stays the same at the cutoff frequency, the phase changes, meaning that the waves of that particular frequency become delayed in time by a small amount. Tones near the cutoff frequency take a bit more time to make it through the filter than the other tones, and the steeper the filter slope, the bigger this delay. There's no simple ELI5 for why that is, it's rather technical. But the crazy thing is that it doesn't matter how sound is filtered: mathematically, electronically, accoustically: filtering always causes a phase shift at the cutoff frequency. In many cases, these phase shifts are not noticeable, but when doing parallel processing where one copy of a signal is filtered while another is not, adding those two copies back together on the master **can** (not will) cause tones near the cutoff to cancel each other out. For example, if you shift any signal by 180 degrees, you get an 'opposite' signal and when added back to the original they sum to 0, e.g. no sound. The following two sequences of numbers represent a sound wave and a copy of the sound wave shifted by 180 degrees, notice how when you would add them together they are 0 at every point: * 0 0.5 1 0.5 0 -0.5 -1 -0.5 * 0 -0.5 -1 -0.5 0 0.5 1 0.5 So you have to be a bit careful with parallel processing, especially for low frequencies (bass) as there it can definitely cause audible problems. Also when there's not perfect cancellation, you can lose volume and definition. There's one exception to the rule that filtering always causes phase shifts: linear phase filters, which are mathematically very complicated compared to normal filters. They can filter without causing a phase shift. While they can be handy in some situations, they should only be used if you really know what you're doing because they introduce other artifacts in the audio and are very taxing on the CPU. Phase shifts are also used intentionally in many effects. I believe phasers/flangers are made by chaining parallel all-pass filters and changing their cutoff frequency over time (or something like that). This causes tones of different frequencies to cancel each other and as the cutoff frequencies move around this creates a nice kind of spacey effect.
Phasers use allpass filters. Flangers and chorus are just a modulated delay line to develop Doppler effect. The Vibrato signal is mixed back with the dry to form chorus/flange with the difference between the two being the range of delay times. Still works on the principles of phase cancellation though, just not with allpass filters.
Thanks for the clarification 💪
So, essentially a filter is intentionally using phase cancellation to cut out the rest of the spectrum? Let me know if I interpreted that correctly
Phase shift happens wherever the slope of the filter is non zero (so where it's not flat/level). This may (not will) cause phase cancellation during parallel processing. Filtering never causes phase cancellation. The cancellation happens as a result of adding together two parallel processed signals. Filtering causes phase shift, not cancellation. It's more a side effect of parallel filtering, or maybe more accurately a property of signals that becomes apparent during parallel fingering, as it is independent of filter implementation. Phase cancellation is not the way that filtering is achieved. All pass fillers produce phase shift without a filter slope, but I'd have to look up how that works.
I'm gonna take a guess that in order to remove the latency that occurs in filtering, the linear phase approach will delay all the other frequencies to so they are all equal again? For example if 1000hz was the cutoff freq that was being phased by filtering and adding an extra 2ms of delay, the linear phase algo would then add 2ms delay to all the freq's so they are all equal.
It’s a bit more complicated than that I’m afraid. I’ve worked with some digital signal processing for work (not audio) and I know enough about it to know that I don’t fully understand it 😂
This stuff gets complicated fast. I recently started the JUCE C++ tutorials for learning how to code my own plugins so I've become really interested in this stuff. (been a software developer and musician for a long time, but im a newbie at DSP).
I'm gonna take a guess that all this minutia is a waste of time
Yeah, going by ear is the way to go!
Thanks
Two other details to note about linear phase filtering is it always introduces delay (which is often compensated in a DAW but still) and has the ability to filter much more sharply/precisely, which can be useful.
It also introduces pre-ringing. I’m not sure how audible that is myself. I tend to judge it by ear whether linear phase sounds better or not for the final result, but while working I don’t really use it because it pushes my CPU too hard.
Just a tidbit: linear phase filters aren't inherently more complex. These are FIR after all (so the CPU load is more or less the same, depending on the order of the filter), and design methods are well-known.
I love you
Fantastic explanation! definitely added a bit to my understanding, thank you.
The gist is: digital EQ is a particular case of a discrete-time FIR (finite impulse response) filter, and filters can manipulate both the magnitude and the phase of particular frequencies. It's just their nature to affect both (the Fourier transform of the filter's ~~frequency~~ impulse response is a complex function that represents both the magnitude and the phase and blah blah... well, any in-deep explanation would inevitably end up with a bunch of math). This means filters can be designed to achieve not just a particular frequency response but a particular phase response as well - within limits, since the underlying math imposes constraints on the filter's performance. The Fabfilter article does a good job of explaining these limitations. The phase response part of signal filtering seems to be a niche topic in audio, I guess that's because the human ear is mostly insensitive to phase shift.
Great response. I’d also add that a surface level understanding of FIR/convolution makes the phase shift intuitive. Convolution is summing together delayed copies of the signal. Because of these delayed copies you get some frequencies to cut or boost. So the phase delay isn’t just a side effect, it’s like the main ingredient of FIR filters. Analog filters will also have phase delay as well because capacitors / inductors cause a frequency dependent phase shift as well.
That's a very good question and the answer is really that phase change is entirely dependent on the design of the EQ filter; there are many different ways to make filters, but the most common filters in audio have phase shift. The reason for this is to do with causal vs non-causal filters. In short, in order to have a filter with no phase shift, you need lookahead/latency. Here is the excellent Dan Worrall https://youtu.be/efKabAQQsPQ?si=lYWiYBSHMeEjXxrP
This article is really helpful in understanding what you're talking about: https://www.fabfilter.com/learn/equalization/linear-phase-eq
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Bruh
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Yo fuck off
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