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# Phase vs. delay

Hello forum.

I have a question that i have not been able to find an answer to. Hope someone can help me.

When looking at a many subwoofers, including my own, I seen that there is a at knob called “phase”. It is either variable or fixed between 0 and 180 degrees.
I understand that what the fixed option will do.- Reverse the direction of the woofer. Right? At least that makes completely sense to me as not all speakers (in my experience) have the same absolute phase. In combination with the delay function In the receiver I can then integrate the speakers and the sub as to be in phase in the listening position.

However I struggle to understand how the variable option works.

Say for instance you set the knob at 0 degrees and you start to plat a sinus tone. At the beginning of the tone the phase and amplitude is 0 and the phase and amplitude (of the amp output) is also 0. To me that make sense and is in accordance with what little I know about the subject. If I set the knob at 90 degrees and start to play the same tone the phase and amplitude is 0, and the phase (of the amp output) is now 90 degrees and the amplitude is now “100%”. Right? To me that is meaningless, so either I don’t really understand or the “phase” knob Is doing something else than.

This leads me to believe that the “phase” knob on a sub with –continuously variable- phase is in reality a delay adjustment. Is that the right assumption?

http://www.indiana.edu/~emusic/acoustics/phase.htm

Dan

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Think of phase as timing, and the function will be clearer.
Thanks Jim

I am not sure how to interpret your answer. Are you saying that I am right in the assumption that the variable phase knob is in reality variable delay?
Quote:
Originally Posted by splotten

Thanks Jim

I am not sure how to interpret your answer. Are you saying that I am right in the assumption that the variable phase knob is in reality variable delay?

In the sense that variable phase varies the woofer response in time, yes.
When you only have one driver, delaying it 90, 180, 270, or 360 degrees wont sound any different. But when you add a second or third driver, then things mater. One driver at 0/360 with another at 180 will cancel (if distances ect are symmetrical). One will be pushing while the other pulls, negating each. Now distances must also come into the equation. Take two drivers at the same phase but at different distances from some given listening position. The difference in distance changes the timing of their wave arrivals putting them out of phase with each other once again.

The variable phase option, usually for subs amps, is so you can align their phase in situations where their distances from the listening position are different. It actually gets more complicated than this given their reflection off of walls come back to the listening position at a different phase, and thus can either create a peak or null at some given frequency(s) depending on the travel distance of the reflection, thus the need for bass trapping to minimize certain reflections.
OK.

I think I got it now…

1) If I have a subwoofer with selectable 0 or 180 degree phase selector, and I set it at 0 degrees, the sub amp will instantly “duplicate” the input on the output, but with larger amplitude? (assuming no other filters)

2) If I have a subwoofer with selectable 0 or 180 degree phase selector, and I set it at 180 degrees, the sub amp will instantly “phase reverse” the input on the output, but with larger amplitude? (assuming no other filters)

3) If I have a subwoofer with variable phase knob, and I set it at 0 degrees, the sub amp will instantly “duplicate” the input on the output, but with larger amplitude? (assuming no other filters)

4) If I have a subwoofer with variable phase knob, and I set it at 90 degrees, the sub amp will “delay” the output, but with larger amplitude (assuming no other filters), and the output will otherwise be identical to the 0 degree setting in (3)?

If (4) is correct, how much delay is introduced. I mean one full cycle at 20Hz is twice as long in time as one full cycle at 40Hz. Let’s say I set the knob at 180 degree. How much delay is introduced?

Edit: Reading post 5# now... Thanks :-)

Dan
Quote:
Originally Posted by jim19611961

When you only have one driver, delaying it 90, 180, 270, or 360 degrees wont sound any different. But when you add a second or third driver, then things mater. One driver at 0/360 with another at 180 will cancel (if distances ect are symmetrical). One will be pushing while the other pulls, negating each. Now distances must also come into the equation. Take two drivers at the same phase but at different distances from some given listening position. The difference in distance changes the timing of their wave arrivals putting them out of phase with each other once again.

The variable phase option, usually for subs amps, is so you can align their phase in situations where their distances from the listening position are different. It actually gets more complicated than this given their reflection off of walls come back to the listening position at a different phase, and thus can either create a peak or null at some given frequency(s) depending on the travel distance of the reflection, thus the need for bass trapping to minimize certain reflections.

The first part of your answer is in complete accordance to my prior understanding. I use the delay function in the receiver to align the phase of subwoofer and the bass driver in the speakers. I leave the phase on the sub alone (0 degrees).

The second part is sort of the answer I was looking for. The way I understand it is that the phase knob on the subwoofer is in reality doing much the same thing as the delay function in the receiver. It is not altering the phase per se. It is delaying the output of the subwoofer to make I possible to -phase align- the sub and the speakers?

Dan
Phase IS delay in this context.

If you have a measurement mic and software to run an ETC, you would be able to see the response in the time domain of each source. And with variable phase, be able to adjust each (theoretically) to converge in phase at the listening position by aligning their peaks.
I appreciate your input, but I am still struggling a bit, and wonder if my messages are somehow unclear.

Lets sat I “send” only one full cycle at 40Hz to the subwoofer and I have the phase set at 0 degrees. To my understanding the sub amp will now instantly reproduce the signal on the output. The amplitude will be bigger but it will still be a one cycle sine wave starting at zero amplitude and ending at zero.

If I now set the phase to 90 degrees, the output of the sub amp will also be a one cycle sine wave starting at zero amplitude, just like before, -but I will be delayed in time. Right??

This to me is the same thing as setting delay in the receiver, but -not- necessarily the same as inverting the phase with a switch on the sub.

If I invert the phase, the output on the sub can be instantaneous, but with the woofer “moving in instead of out” (or vice versa).

Dan
Quote:
Originally Posted by splotten

I appreciate your input, but I am still struggling a bit, and wonder if my messages are somehow unclear.

Lets sat I “send” only one full cycle at 40Hz to the subwoofer and I have the phase set at 0 degrees. To my understanding the sub amp will now instantly reproduce the signal on the output. The amplitude will be bigger but it will still be a one cycle sine wave starting at zero amplitude and ending at zero.

If I now set the phase to 90 degrees, the output of the sub amp will also be a one cycle sine wave starting at zero amplitude, just like before, -but I will be delayed in time. Right??

This to me is the same thing as setting delay in the receiver, but -not- necessarily the same as inverting the phase with a switch on the sub.

If I invert the phase, the output on the sub can be instantaneous, but with the woofer “moving in instead of out” (or vice versa).

Dan

In truth, phase as it applies to HT receivers is not my strength (never owned one). I used to have a Yamaha DSP-1 processor, but its delays were designed for room ambiance, not phase alignments. This may be the case with your receiver also. Admittedly, I am not sure. Someone with expertise with HT receivers could probably get this more right than I am.
Edited by jim19611961 - 2/10/13 at 12:10pm
Phase is a relative measurement, relative to a known, unshifted wave, and it's measured in degrees.

Quite different from time delay, phase, ... once shifted either backward or forward 360 degrees, results the same as not shifting it at all.

Time delay, represents how far in seconds a wave must be shifted to align it with a known reference. Time delay is just that, a shift in time relative to an unshifted wave.

Be mindful that the amount of phase shift that equates to a given time shift, entirely depends on the frequency wave.
Quote:
Originally Posted by FOH

Phase is a relative measurement, relative to a known, unshifted wave, and it's measured in degrees.

Quite different from time delay, phase, ... once shifted either backward or forward 360 degrees, results the same as not shifting it at all.

Time delay, represents how far in seconds a wave must be shifted to align it with a known reference. Time delay is just that, a shift in time relative to an unshifted wave.

Be mindful that the amount of phase shift that equates to a given time shift, entirely depends on the frequency wave.

All of the above makes complete sense to me.

However I still feel that I don’t get my message across. At least I don’t really feel enlightened yet. Please bear with me ;-)

Think of my question this way:

Assuming 1Hz and the knob set at 0 degrees

If we look at the one cycle sine wave once again. When the cycle begins at time t=0 seconds, the phase is 0 and the amplitude is also 0 on both the input and the output of the amplifier. At 0,25s the phase is 90degrees and the amplitude is “1”, on both the input and the output of the amplifier. At 0,5s the phase is 180 degrees and the amplitude is again 0, on both the input and the output of the amplifier. And so forth….

Still assuming 1Hz and the knob set at 90 degrees:

When the cycle begins at time t=0 seconds, the phase is 0 and the amplitude is also 0 on the input. If setting the phase knob to something other than 0 implies -no time shift- the output (amplitude) at t=0 is now shifted 90 degrees and must therefore be “1” instead of 0. This seems unlikely.

Dan
Edited by splotten - 2/10/13 at 12:05pm
Quote:
Originally Posted by FOH

Phase is a relative measurement, relative to a known, unshifted wave, and it's measured in degrees.

Quite different from time delay, phase, ... once shifted either backward or forward 360 degrees, results the same as not shifting it at all.

Time delay, represents how far in seconds a wave must be shifted to align it with a known reference. Time delay is just that, a shift in time relative to an unshifted wave.

Be mindful that the amount of phase shift that equates to a given time shift, entirely depends on the frequency wave.

This is where I wasnt clear. Actually, a phase shift is a time delay, but on a different scale than what an AV receiver is calling "time delay". Right?
There is a wealth of information on sub woofer integration somewhere on this forum. Also search for member Wayne Ph......, I don't remember the last name but it was unusual. He knows a lot about this.

I gotta tell you I followed the sub woofer calibration advice a few years ago and it made a huge difference in my system.
Quote:
Originally Posted by Glimmie

There is a wealth of information on sub woofer integration somewhere on this forum. Also search for member Wayne Ph......, I don't remember the last name but it was unusual. He knows a lot about this.

I gotta tell you I followed the sub woofer calibration advice a few years ago and it made a huge difference in my system.

Yes i know :-) Thanks.

I could not find the answer to my question though. In reality it is more like a technical question than a practical one.

Dan
Quote:
Originally Posted by splotten

Assuming 1Hz and the knob set at 0 degrees

If we look at the one cycle sine wave once again. When the cycle begins at time t=0 seconds, the phase is 0 and the amplitude is also 0 on both the input and the output of the amplifier. At 0,25s the phase is 90degrees and the amplitude is “1”, on both the input and the output of the amplifier. At 0,5s the phase is 180 degrees and the amplitude is again 0, on both the input and the output of the amplifier. And so forth….

Still assuming 1Hz and the knob set at 90 degrees:

When the cycle begins at time t=0 seconds, the phase is 0 and the amplitude is also 0 on the input. If setting the phase knob to something other than 0 implies -no time shift- the output (amplitude) at t=0 is now shifted 90 degrees and must therefore be “1” instead of 0. This seems unlikely.

Dan
The quandary there is that you are describing a digital boundary condition rather than a steady state analog system. When you suddenly turn something on, in that instant the system behavior may be wrong or undefined. Since we don't have negative time, the phase shift can't do what it normally does which is to present what had happened in the past. Fortunately once we travel into time the system snaps into correct behavior and all is well. In your example, you have to examine system behavior once you arrive at 90 degrees relative to the original signal start time.

Digital systems are notorious for having the wrong output in such situations. Think of a digital filter that needs past and present samples to do its thing. Clearly when "life starts" it has no past samples so what the system puts out is incorrect for a few samples. Pops, noises and glitches when you turn such systems on are the manifestations of these (well designed systems mute the output or have other mitigations).

Hope this clarifies things rather than make them more complicated .
I'm having a difficult time figuring out how a true "phase" control on a sub would be of much use. Phase shifting a 50 Hz sine wave by 90 degrees does not phase shift a 120 Hz sine wave by the same amount. Here's an example. The top plot shows a signal consisting of a 50 Hz sine and a 120 Hz sine. The green plot is the same signal time delayed by 5 ms. Same signal, just shifted.

This one shows the same 50 Hz sine and a 120 Hz sine (blue trace), and this time that signal is phase shifted by 90 degrees (green trace). 90 Degrees happens to be 5 ms for a 50 Hz signal, but a 90 degree phase shift for a 120 Hz signal is 2.1 ms.

The point being, a phase shift is NOT the same as a time delay. However, I have a hunch that the "phase" knob on your sub IS just a time delay. Hopefully somebody can answer this definitively.
Quote:
Originally Posted by J_P_A

The point being, a phase shift is NOT the same as a time delay. However, I have a hunch that the "phase" knob on your sub IS just a time delay. Hopefully somebody can answer this definitively.
I can't answer this definitively either, but I was thinking the same thing. I would bet that when a knob is labeled as "phase", it is either marked in degrees for only one frequency, or not marked in degrees at all.

The reason I think this is because I don't know of any circuit or DSP algorithm that can adjust the phase of all frequencies in a band by the same angle. On the other hand, it is trivial to delay all frequencies by the same variable amount of time in a DSP.
Its almost certainly a phase knob because odds are vastly in favor of it being an analog circuit. Time delay with analog is possible but complex and won't be found in a consumer sub. I suppose a few digital dsp powered subs are out there now, but odds are still against it.

True time delay is the preferred method as it keeps all frequencies in phase even if the speakers are offset by some distance. This is what all modern avr's use.

But phase can be a decent substitute for sub duty. The reason this works is the crossover starts rolling the highs off below xo frequency, and sub behavior dominates. Also, sub rolls off above xo frequency, so mains behavior dominates. Phase shifting the sub will cause a mismatch at frequencies other than the xo frequency, the mismatch getting larger for frequencies further above or below the xo, but again the further away from xo you get the more only one speaker or the other contributes to the composite. Thus, getting the phase matched at the xo frequency is a pretty good substitute for true time delay.

At least, that's how t it works on paper. Put a real sub in a real room and ideal goes out the window. At that point, the proper solution is the one that happens to work. No kidding. Just ask jbl... their latest and greatest sub processing can be summarized well enough as "try everything, and keep whatever happens to measure better..."
So from what I can gather from all of your posts are that phase shift is definitely not the same as a time delay, and that a phase shift circuit will introduce phase shifts into the audio signal itself. This might or might not be audible according to various posts found elsewhere, but is IMO best avoided if possible.
The better solution seems to be a true time shift to align the phase of the sub and speakers. This is readily available in the receiver.

I am not able to tell if the sub is “digital” or analog with confidence, but I opened it up and looking at the plate amp, my guess is that it is in fact digital. By the look of the input circuit it looks like some sort of imbedded DSP. I guess it is possible to execute both time shift and phase shift in the digital domain (thanks amirm) but without measuring the output I can’t know for sure. My best guess is that it is a phase shift circuit as it is clearly marked with settings for different degrees. As such I conclude for now that the phase knob is best left at zero and that I’m better off using the delay function in the receiver.

At least I can not imagine why I would need phase shift when delay is possible in my setup.

Dan
Quote:
Originally Posted by splotten

So from what I can gather from all of your posts are that phase shift is definitely not the same as a time delay,

The two are closely related. For example, a time delay that is constant for various frequencies, introduces a readily-predictable phase shift that varies with frequency.

For example a time delay of 1 milliseconds at all relevant frequencies introduces 90 degrees of phase shifit at 250 Hz, 180 degrees at 500 Hz, and 360 degrees at 1,000 Hz.

Most analog circuits produce a phase shift that inherently varies with frequency in a way that differs from that produced by a straight broadband delay.
Quote:
a phase shift circuit will introduce phase shifts into the audio signal itself.

As long as the phase shift is signficant at audible frequencies. For example a circuit could cause 90 degrees of phase shift at 1 GHz. That would be 9 degrees at 100 MHz, 0.9 degrees at 10 MHz, 0.09 degrees at 1 MHz, 0.009 degrees at 100 KHz, and 0.0009 degrees at 10 KHz. Obviously the phase shift in the audio band is negligable for practical purposes.
Quote:
This might or might not be audible according to various posts found elsewhere, but is IMO best avoided if possible.

The amount of phase shift that is audible depends on the amount of phase shift, the frequency of the signal, and whether or not the phase shift is applied equally to all audible sources or not.
Quote:
The better solution seems to be a true time shift to align the phase of the sub and speakers. This is readily available in the receiver.

In general, probably true.

In general, it seems better to rely on the delay function in your AVR as it is likely to be the cleaner implementation of the effect.
Quote:
Originally Posted by J_P_A

The point being, a phase shift is NOT the same as a time delay. However, I have a hunch that the "phase" knob on your sub IS just a time delay. Hopefully somebody can answer this definitively.
I am not sure how definitive my answer is as I am not a subwoofer designer . But as far as I know, they use an all-pass filter. If you have not heard of that, this is a filter that has unity gain (constant amplitude) but a phase that varies with frequency (it is a combination of a low pass and high pass filter). The variation follows an arctan curve which is mostly linear (in log scale) for some of its region. Here is an example graph for an all pass filter I randomly found:

The shape of that graph can be modified by the "order" of the all pass filter and its (Fc) parameters. But as you can see, for a limited range around that center frequency (10 KHz in the graph above), one can get a linear (in log scale) relationship where the phase proportionally changes with frequency giving us a delay circuit as you correctly state.
http://www.sengpielaudio.com/calculator-soundpath.htm

Here is a link to a Time vs Distance calculator. Might find it handy.
Quote:
Originally Posted by amirm

....... But as you can see, for a limited range around that center frequency (10 KHz in the graph above), one can get a linear (in log scale) relationship where the phase proportionally changes with frequency giving us a delay circuit as you correctly state.

Agreed, a time delay results in a frequency dependent phase shift.

F{ x(t-T) } = X(w)e(-jwT)

I've recently become more familiar with the uses of all-pass filters in audio as they are used for decorrelation as well. But the question remains, what processing is being done based on the position of that "phase" knob. If they are just introducing a time delay (either by processing in the temporal of frequency domain) then why isn't the knob labeled "delay?" If they are truly adjusting the phase of the signal, then shouldn't there be some documentation with regard to what frequency is being used as the center frequency? Seems shady to me
Much good info:)

I won’t pretend to understand all of it fully, so I will let it “stew” for a while.

Let me just ask you guys a clarifying question :

If I send an audio signal through a phase filter/all pass filter. The output of the Will look different than the input. - As in I won’t be able to overlay one with the other and easily see that one came from the other. Right?

If I send the same audio signal through a receiver with a delay function and set it to unity gain. The output will be identical but shifted in time. Right?

I conclude this from the pictures posted above.

Dan
Quote:
Originally Posted by splotten

Much good info:)

If I send an audio signal through a phase filter/all pass filter. The output of the Will look different than the input. - As in I won’t be able to overlay one with the other and easily see that one came from the other. Right?

This may or may not be true. There are many kinds of phase shifters. The ones called "Linear Phase" function like true time delays and don't distort the wave form.

However in most other cases, what you say will be true.
Quote:
If I send the same audio signal through a receiver with a delay function and set it to unity gain. The output will be identical but shifted in time. Right?

This is always true.
Quote:
Originally Posted by J_P_A

Quote:
Originally Posted by amirm

....... But as you can see, for a limited range around that center frequency (10 KHz in the graph above), one can get a linear (in log scale) relationship where the phase proportionally changes with frequency giving us a delay circuit as you correctly state.

Agreed, a time delay results in a frequency dependent phase shift.

F{ x(t-T) } = X(w)e(-jwT)

I've recently become more familiar with the uses of all-pass filters in audio as they are used for decorrelation as well. But the question remains, what processing is being done based on the position of that "phase" knob. If they are just introducing a time delay (either by processing in the temporal of frequency domain) then why isn't the knob labeled "delay?" If they are truly adjusting the phase of the signal, then shouldn't there be some documentation with regard to what frequency is being used as the center frequency? Seems shady to me

The time delay knobs on subwoofers appear to usually be implemented in the analog domain and are some kind of an analog phase shifter.

If you play with the Q of a second-order all-pass you can obtain a fairly wide region of frequencies where it acts like a delay.

Since subwoofers operate over a relatively narrow band of frequencies, a phase shifter that reasonably closely approximates a time delay seems more possible.
Edited by arnyk - 2/11/13 at 1:50pm
Hi Amir,
Quote:
Originally Posted by amirm

I am not sure how definitive my answer is as I am not a subwoofer designer . But as far as I know, they use an all-pass filter. If you have not heard of that, this is a filter that has unity gain (constant amplitude) but a phase that varies with frequency (it is a combination of a low pass and high pass filter). The variation follows an arctan curve which is mostly linear (in log scale) for some of its region.

The shape of that graph can be modified by the "order" of the all pass filter and its (Fc) parameters. But as you can see, for a limited range around that center frequency (10 KHz in the graph above), one can get a linear (in log scale) relationship where the phase proportionally changes with frequency giving us a delay circuit as you correctly state.
Your description of the all-pass filter is correct, and maybe the best method when you're restricted to the analog domain. However, I don't think it is how the delay would be created in a digital world, where a much better algorithm exists: the digital delay-line.

A digital delay, when implemented in a DSP, takes almost no processing power and has a perfectly linear phase response. It does require more memory than an all-pass filter, but only a modest amount. I mention the technique here: http://www.avsforum.com/t/1281290/minidsp/1410#post_22924708 in the miniDSP thread.
A true time delay in the digital domain just needs a simple shift register (memory). The tricky part arises when you want to compensate for non-ideal components like speaker crossovers and need an actual compensatory phase shift; that requires a more complex filter. Time-aligning all frequencies, is that required? I spent years making sure my speakers had good pulse response, but I am honestly not sure how important that is in the real world.
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