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Post by matt@IAA on May 10, 2021 8:01:01 GMT -6
Group delay is not the same as phase shift but they are related. Actually group delay is the first derivative of phase with respect to frequency. It is not a phase shift, at least not the way we're talking about it here. And this is why things get so confusing!!
Again for my poor ME brain I have to go back to physical systems. 0 degrees for me is a location on a rotor, top dead center on an engine, something like that.. you could say 0 degrees is defined by zero amplitude at 1kHz in the source signal, for example. A phase shift when we're talking about a filter is a reference to the change in time of that zero amplitude relative to the reference signal. That time is defined by the period of the signal we're looking at. It's always a comparative thing.
A time delay is a constant lag of the entire waveform at all frequencies from DC to infinity. This is also a phase shift, but the number of degrees each particular frequency is shifted varies as a function of the frequency. A time delay is a group delay of constant value in seconds.
In the same way that speed is the rate of change of position with respect to time, group delay is the rate of change of phase with respect to frequency. Group delay and phase are dp/dw where p is phase angle phi and w is omega, frequency. Remember when you integrate you get a constant. So a zero phase rate of change integrated over all frequencies can still have a group delay in that constant term, a constant offset. That would be a pure delay, where all frequencies move together by a fixed amount of time.
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Post by Guitar on May 10, 2021 8:04:51 GMT -6
Brilliant, thank you! Edit: I believe group delay is also measured in seconds.
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Post by svart on May 10, 2021 8:39:50 GMT -6
Group delay is not the same as phase shift but they are related. Actually group delay is the first derivative of phase with respect to frequency. It is not a phase shift, at least not the way we're talking about it here. And this is why things get so confusing!! Again for my poor ME brain I have to go back to physical systems. 0 degrees for me is a location on a rotor, top dead center on an engine, something like that.. you could say 0 degrees is defined by zero amplitude at 1kHz in the source signal, for example. A phase shift when we're talking about a filter is a reference to the change in time of that zero amplitude relative to the reference signal. That time is defined by the period of the signal we're looking at. It's always a comparative thing. A time delay is a constant lag of the entire waveform at all frequencies from DC to infinity. This is also a phase shift, but the number of degrees each particular frequency is shifted varies as a function of the frequency. A time delay is a group delay of constant value in seconds. In the same way that speed is the rate of change of position with respect to time, group delay is the rate of change of phase with respect to frequency. Group delay and phase are dp/dw where p is phase angle phi and w is omega, frequency. Remember when you integrate dx/dt you get x+C. So a zero phase rate of change integrated over all frequencies can still have a group delay in that C term, a constant offset. That would be a pure delay, where all angles move together by a fixed amount of time. There is also "phase delay" which describes the difference in time delay over frequency and can define the phase shift at any singular frequency. In practice, Group Delay is generally thought of as the time delay through a complex circuit of the frequency components of a modulated signal, so it's usually a defined frequency domain bandwidth, but it also changes the integral of the phase/frequency so we're back to looking at what are we trying to measure?For those who don't want math (I don't either): Group delay measures the time delay of frequency components in a signal, usually bounded by a given bandwidth. It expects that phase relationships are maintained through the circuit because the time delay is equal. Phase delay is simply the delay in time that a frequency experiences through a circuit. Phase shift is the amount of phase change a signal experiences through a circuit. This can be measured as absolute (phase difference in output compared to input) or relative (to surrounding frequencies). Time, phase and frequency are interlinked much like volts, resistance and current are. You can't change one without the others changing as well. EDIT: "What are we trying to measure" is kind of an in-joke for me. Having worked for a handful of high caliber folks, there has always been quite a lot of, uh, "spin" or "self promotion" around architecting designs and folks rarely just get to the point. I suppose that's why I'm always explaining things like a layman.
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Post by Guitar on May 10, 2021 10:21:27 GMT -6
The laymen around here really appreciate it, thanks svart.
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Post by ragan on May 10, 2021 11:09:12 GMT -6
In the same way that speed is the rate of change of position with respect to time, group delay is the rate of change of phase with respect to frequency. Group delay and phase are dp/dw where p is phase angle phi and w is omega, frequency. Remember when you integrate you get a constant. I'm not quite following this. Are you talking about evaluating a bounded, definite integral (to get a constant out of it)? Because if not, integration would usually get you a (scaled) higher power version of the function, wouldn't it? Or, if sinusoidal, a shifted version. Differentiation would get you a constant if it's with respect to a variable that's only to a power of one in the function. Or, wait, do you mean the arbitrary constant you need in order to have a valid anti-derivative in a general sense (which just allows for any vertical shift we might need to correctly describe the behavior)? Or maybe I'm missing what you're saying altogether.
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Post by Pueblo Audio on May 10, 2021 13:45:25 GMT -6
When we watch football, we measure the balls movements in yards. When we measure the diameters of vinyls discs we measure in inches. We use the most fitting unit of measure most appropriate to the scale of the situation.
When talking about FX delays in music (echos, guitar pedals) the scale lends to be expressed in seconds or milliseconds. When we talk about DSP latency the scale is in samples. When we talk about signal delays who’s durations are comparable to the wavelength of a signal, the scale is in degrees of phase. It takes 360 degrees to complete one cycle, or phase, of a periodic waveform (like a sine wave).
For example, take ‘A’ 440Hz which is 440 cycles per second. One complete cycle has a wavelength of 2.27ms. If we divide one cycle by 360 degrees then one degree = .0063ms. (Your not gonna hear kind of delay in a balloon pop video so forget that red herring). Because of the scale, it can be easier here to express in degrees and avoid the decimal places.
Now back to phase SHIFT. This is always a relative term. For HPF we are interested in the phase shift (small time delay) of the overtones *RELATIVE* to their fundamental. We are interested because this is a real and audible form of distortion called Deviation from Linear Phase.
Without the HPF the overtones are time aligned to their fundamental (Linear Phase). But with a HPF the overtones get shifted in time (measured in degrees). Each overtone will become misaligned , more and more, depending on their frequency. 2nd partial more than the first, 3rd more than the 2nd, and so on. Take note that these hollowed, smeared tonalities will be heard ABOVE the cut off frequency!
I hope that helps
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Post by matt@IAA on May 10, 2021 14:50:56 GMT -6
In the same way that speed is the rate of change of position with respect to time, group delay is the rate of change of phase with respect to frequency. Group delay and phase are dp/dw where p is phase angle phi and w is omega, frequency. Remember when you integrate you get a constant. I'm not quite following this. Are you talking about evaluating a bounded, definite integral (to get a constant out of it)? Because if not, integration would usually get you a (scaled) higher power version of the function, wouldn't it? Or, if sinusoidal, a shifted version. Differentiation would get you a constant if it's with respect to a variable that's only to a power of one in the function. Or, wait, do you mean the arbitrary constant you need in order to have a valid anti-derivative in a general sense (which just allows for any vertical shift we might need to correctly describe the behavior)? Or maybe I'm missing what you're saying altogether. Arbitrary constant in general sense. But you could have a completely zero group delay (no rate of change of phase wrt frequency) but a constant time offset. Math still works.
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Post by gravesnumber9 on May 10, 2021 14:53:19 GMT -6
When we watch football, we measure the balls movements in yards. When we measure the diameters of vinyls discs we measure in inches. We use the most fitting unit of measure most appropriate to the scale of the situation. When talking about FX delays in music (echos, guitar pedals) the scale lends to be expressed in seconds or milliseconds. When we talk about DSP latency the scale is in samples. When we talk about signal delays who’s durations are comparable to the wavelength of a signal, the scale is in degrees of phase. It takes 360 degrees to complete one cycle, or phase, of a periodic waveform (like a sine wave). For example, take ‘A’ 440Hz which is 440 cycles per second. One complete cycle has a wavelength of 2.27ms. If we divide one cycle by 360 degrees then one degree = .0063ms. (Your not gonna hear kind of delay in a balloon pop video so forget that red herring). Because of the scale, it can be easier here to express in degrees and avoid the decimal places. Now back to phase SHIFT. This is always a relative term. For HPF we are interested in the phase shift (small time delay) of the overtones *RELATIVE* to their fundamental. We are interested because this is a real and audible form of distortion called Deviation from Linear Phase. Without the HPF the overtones are time aligned to their fundamental (Linear Phase). But with a HPF the overtones get shifted in time (measured in degrees). Each overtone will become misaligned , more and more, depending on their frequency. 2nd partial more than the first, 3rd more than the 2nd, and so on. Take note that these hollowed, smeared tonalities will be heard ABOVE the cut off frequency! I hope that helps So this sounds like the issue is worse the lower the frequency, right? If it's a cascading effect with each overtone. So, for example, an aggressive LPF might be less likely to cause such issues.
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Post by ragan on May 10, 2021 14:54:28 GMT -6
I'm not quite following this. Are you talking about evaluating a bounded, definite integral (to get a constant out of it)? Because if not, integration would usually get you a (scaled) higher power version of the function, wouldn't it? Or, if sinusoidal, a shifted version. Differentiation would get you a constant if it's with respect to a variable that's only to a power of one in the function. Or, wait, do you mean the arbitrary constant you need in order to have a valid anti-derivative in a general sense (which just allows for any vertical shift we might need to correctly describe the behavior)? Or maybe I'm missing what you're saying altogether. Arbitrary constant in general sense. But you could have a completely zero group delay (no rate of change of phase wrt frequency) but a constant time offset. Math still works. Word. Like a phase bias.
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Post by stormymondays on May 10, 2021 14:59:55 GMT -6
Today I had the rare occasion to remix a track that I had mixed for a time sensitive project that didn’t come to be. So, instead of recalling all the hardware, I took the chance of taking off all the HPF and redo the mix from almost scratch. I’m liking it!!! I’ll let you know if it turns into a muddy mess or if it gets that huge deep sound I’m chasing after...
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Post by svart on May 10, 2021 15:05:40 GMT -6
When we watch football, we measure the balls movements in yards. When we measure the diameters of vinyls discs we measure in inches. We use the most fitting unit of measure most appropriate to the scale of the situation. When talking about FX delays in music (echos, guitar pedals) the scale lends to be expressed in seconds or milliseconds. When we talk about DSP latency the scale is in samples. When we talk about signal delays who’s durations are comparable to the wavelength of a signal, the scale is in degrees of phase. It takes 360 degrees to complete one cycle, or phase, of a periodic waveform (like a sine wave). For example, take ‘A’ 440Hz which is 440 cycles per second. One complete cycle has a wavelength of 2.27ms. If we divide one cycle by 360 degrees then one degree = .0063ms. (Your not gonna hear kind of delay in a balloon pop video so forget that red herring). Because of the scale, it can be easier here to express in degrees and avoid the decimal places. Now back to phase SHIFT. This is always a relative term. For HPF we are interested in the phase shift (small time delay) of the overtones *RELATIVE* to their fundamental. We are interested because this is a real and audible form of distortion called Deviation from Linear Phase. Without the HPF the overtones are time aligned to their fundamental (Linear Phase). But with a HPF the overtones get shifted in time (measured in degrees). Each overtone will become misaligned , more and more, depending on their frequency. 2nd partial more than the first, 3rd more than the 2nd, and so on. Take note that these hollowed, smeared tonalities will be heard ABOVE the cut off frequency! I hope that helps So this sounds like the issue is worse the lower the frequency, right? If it's a cascading effect with each overtone. So, for example, an aggressive LPF might be less likely to cause such issues. Phase shift is worse as you rise in frequency if the shift in time (delay) is equal across all frequencies. Lower frequencies have longer wavelengths so a small percentage of phase shift in relation to the frequency's period would be a much higher percentage for a shorter wavelength's period.
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Post by Ward on May 10, 2021 15:47:33 GMT -6
As far as I know, our ears are not sensitive to phase by itself - SNIP But . . . our ears are sensitive to comb filtering and phase cancelation.
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Post by gravesnumber9 on May 10, 2021 15:59:00 GMT -6
So this sounds like the issue is worse the lower the frequency, right? If it's a cascading effect with each overtone. So, for example, an aggressive LPF might be less likely to cause such issues. Phase shift is worse as you rise in frequency if the shift in time (delay) is equal across all frequencies. Lower frequencies have longer wavelengths so a small percentage of phase shift in relation to the frequency's period would be a much higher percentage for a shorter wavelength's period. Maybe I got it backwards. Or maybe I didn't say it right. What I'm saying is that if my EQ is applied at, say, 10khz, that would be less impactful in terms of phase shift because it's only the frequencies above that that get impacted, correct? Or is it still worse because of the shorter wavelength. Just kind of wondering if there's a "safer" EQ range in terms of drastic boosts/cuts. And yes, I get that it's really all just what sounds good is good and that some phase shifts might sound good... still wondering though.
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Post by jmoose on May 10, 2021 18:04:53 GMT -6
Well this has certainly taken a turn into some deep technical stuff that makes my eyes glaze over like I'm sitting in calculus class again.
I don't have any reference on designing circuits or programming plugins... I'm just a simple caveman who's been living in studios & making records for 20 years.
From a practical perspective, when recording guitars I can easily say my favorite EQ in the room... the best, meaning the least offensive and most effective available for that situation is the EQ on the amp head. The second best EQ is moving the microphone.
Seems that for whatever reasons when I need to turn to outboard EQ, the usual suspects to make a sound at a certain point things get weird. And sometimes offensive, like sand on my ears.
Don't get me wrong sometimes I use the whole range and go +15... it's available for a reason but not everything sounds good there and I'm just as happy to not need it.
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Post by Guitar on May 10, 2021 18:22:41 GMT -6
As far as I know, our ears are not sensitive to phase by itself - SNIP But . . . our ears are sensitive to comb filtering and phase cancelation.
Yes I think that's Pueblo's sort of implicit point, the passband of your audio will have a nonlinear phase due to using even a low frequency high pass filter, and you can hear it. But it's up to us of course to assign a value to that, in terms of musical pleasure, which is where this journey started. There are even some plugin makers, well TDR is the example, giving you a Phi button on Slick EQ to totally screw your low end phase response intentionally. They say it can help some material. It's kind of extreme sounding, but it's something to listen to. Sometimes a very steep HPF, 96 dB per octave, etc, helps certain instruments in a mix a lot for me, and you can be certain that it's having a drastic effect on the phase, but it sounds good.
Any phase change in a sine wave (one simple frequency) would just sound like delay. Any phase change of a complex signal with multiple frequencies would be audible, in terms of frequency masking, I think is what Matt ended up saying. Or if I remember correctly, listen to a BBE Sonic Maximizer on but set flat. If you want a really easy way to hear this, and it is easy, just mess with Airwindows Phase Nudge, which is an all-pass filter, meaning it only alters phase and has no effect on EQ. I use this sometimes to fix my vocal headphone feed, to get the phase aligned with my bone conducted head voice, compared to the headphones. Sometimes these processors are also called "phase scramblers."
I believe comb filtering is a form of phase cancellation, if I'm not mistaken, from two identical signals with a slight delay on one of them. Like a flanger, or tape flanging.
What I'm saying is I agree with you, LOL.
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Post by Ward on May 10, 2021 20:00:01 GMT -6
Well this has certainly taken a turn into some deep technical stuff that makes my eyes glaze over like I'm sitting in calculus class again.SNIP Well, sorry not sorry about that. I poked the bear on this one because I really wanted to learn something and I sure did!! I truly appreciate those technical minds who chimed in and gave us all some school (not as bad as calculus). You all are wonderful people!! one last thing . . . Can anyone please weigh in on how phase shift correlations differ in HPF versus bandpass filtering? (I can shut up if I'm pressing too far. )
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Post by Guitar on May 10, 2021 20:10:13 GMT -6
Can anyone please weigh in on how phase shift correlations differ in HPF versus bandpass filtering? (I can shut up if I'm pressing too far. )Here's a graph of a bandpass filter phase response:
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ericn
Temp
Balance Engineer
Posts: 14,921
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Post by ericn on May 10, 2021 21:21:24 GMT -6
Well this has certainly taken a turn into some deep technical stuff that makes my eyes glaze over like I'm sitting in calculus class again.SNIP Well, sorry not sorry about that. I poked the bear on this one because I really wanted to learn something and I sure did!! I truly appreciate those technical minds who chimed in and gave us all some school (not as bad as calculus). You all are wonderful people!! one last thing . . . Can anyone please weigh in on how phase shift correlations differ in HPF versus bandpass filtering? (I can shut up if I'm pressing too far. )It’s going to vary depending on the type/ order/ slope.
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Post by ragan on May 10, 2021 21:30:08 GMT -6
As far as I know, our ears are not sensitive to phase by itself - SNIP But . . . our ears are sensitive to comb filtering and phase cancelation. Comb filtering and phase cancellation rely on there being multiple signals interacting with each other (the original and the reflected, in the case of comb filtering). So you're right, we totally hear that. What (I think) Matt was talking about was single sources which aren't interacting with any others, so there's no opportunity for constructive/destructive interference.
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Post by jmoose on May 10, 2021 22:17:18 GMT -6
It’s going to vary depending on the type/ order/ slope. Yes... which is why at a certain point tech talk is irrelevant to the real world results of you know, actually making records. Take something simple on paper. Going -6dB at 100 cycles. That move on a GML 8200, 1073, and EQP ? All sound & respond completely different... And lurking in the room is an 800 pound gorilla named monitoring. Can we actually hear what's happening? Even if it can't be identified we might still, and probably should have a reaction.
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Post by jcoutu1 on May 11, 2021 7:47:02 GMT -6
But . . . our ears are sensitive to comb filtering and phase cancelation. Comb filtering and phase cancellation rely on there being multiple signals interacting with each other (the original and the reflected, in the case of comb filtering). So you're right, we totally hear that. What (I think) Matt was talking about was single sources which aren't interacting with any others, so there's no opportunity for constructive/destructive interference. The single source is interacting with itself though, right? If there is slight shift at 100Hz, that will interact at 200, 400, 800 etc right?
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Post by svart on May 11, 2021 8:15:27 GMT -6
Phase shift is worse as you rise in frequency if the shift in time (delay) is equal across all frequencies. Lower frequencies have longer wavelengths so a small percentage of phase shift in relation to the frequency's period would be a much higher percentage for a shorter wavelength's period. Maybe I got it backwards. Or maybe I didn't say it right. What I'm saying is that if my EQ is applied at, say, 10khz, that would be less impactful in terms of phase shift because it's only the frequencies above that that get impacted, correct? Or is it still worse because of the shorter wavelength. Just kind of wondering if there's a "safer" EQ range in terms of drastic boosts/cuts. And yes, I get that it's really all just what sounds good is good and that some phase shifts might sound good... still wondering though. Oh ok, I see what you're saying now. Analog EQ works by shifting phase, but the order of the filter determines how quickly the phase is shifted to 180 degress and therefor nullifying. It's important to note that filters are physical things. Math can use phase to describe and determine frequency and rolloff characteristics but so can using charge transfer/capacitance reactance equations or current/time or any number of ways to look at it. There's even ways to figure this stuff out using different types of math such as calculus and algebra and you'll find folks that prefer doing things in different ways too. Personally I excelled at algebra so just about everything I do comes from algebraic equations and I avoid calculus whenever possible, lol.
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Post by svart on May 11, 2021 8:44:45 GMT -6
Also, an interesting side note. One might say "but if a filter shifts phase to nullification, wouldn't it continue to shift until it doesn't?"? The reality is YES. Many filters will eventually have phase shifted so that another pass band will appear at much higher frequencies, usually well outside the range of interest. However, the parasitic effects of the transmission lines also create their own filtering effect, so it's rare to see the phenomenon. In cases where the transmission medium is high enough in bandwidth to see the filter effects in their entirety, it's also a place where one of the filter poles is used to snuff frequencies well outside the band of interest. It's not usually a problem in audio since the bandwidth is so tiny compared to things like RF spectrum where the bandwidths need to be clean as to not interfere with other allotted frequency ranges. Take this guy for instance. It's a 1.8G LPF made from a cascading multiple poles of LC, perhaps on the order of 15-20 poles. You'll notice that the rolloff at 1.8GHz is high, but then it meanders back up around 6-7GHz. This can be modeled as the phase of each LP pole finally returning to a value that does not nullify.
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Post by ragan on May 11, 2021 8:47:15 GMT -6
Comb filtering and phase cancellation rely on there being multiple signals interacting with each other (the original and the reflected, in the case of comb filtering). So you're right, we totally hear that. What (I think) Matt was talking about was single sources which aren't interacting with any others, so there's no opportunity for constructive/destructive interference. The single source is interacting with itself though, right? If there is slight shift at 100Hz, that will interact at 200, 400, 800 etc right? It’s a single source originally but the reason we hear anything related to phase issues is that it reflects off a surface and arrives at different times, blending with the original source that also hits our ears directly, without reflection. So if you were sitting in an anechoic chamber, no comb filtering and no phase funny business. I was just pointing out that it’s the interactions that we hear, not the phase of a single source by itself.
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Post by matt@IAA on May 11, 2021 8:51:45 GMT -6
I suppose if there is a fundamental below the filter with harmonic content above the filter you could end up with out-of-phase higher order products. Practically speaking I don't know what you do with that information or how you use it though - haha.
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