Define "phase"? Or is it polarity?

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Polarity inversion is exactly what the name suggests, it is a change of electrical polarity; what was a negative voltage is now a positive voltage, and vice versa.
Mathematically and simply put it's

V2 = V1 * -1

where V2 is the voltage after inversion and V1 is the original voltage. In other words, simply take the voltage value at every point in the waveform and multiply it by -1 to get the inverted voltage value.

Phase is a bit more complicated in that, like an angle, it can have a value of anywhere from 1° to 360° (or 0°). This is why the change in phase value is commonly referred to as "phase angle". The math involved includes square roots of tangents and stuff like that, which is probably beyond what's wanted here.

But to simplify for this discission, a "phase inversion" is basically an instantaneous (no time shift) phase change of 180°. This resembles a polarity inversion in that an instantaneous 180° phase change does invert the direction up or down of the wave rests, but there is a technical difference:

A polarity inversion, by definition, inverts or flips the wave around the horizontal axis of 0 volts DC. A phase inversion inverts or flips the wave around whatever the rest voltage of the signal may be (the rest voltage being whatever the DC voltage may be during silence.) Put mathematically, phase inversion can be represented by

V2 = (V1 * -1) + VDC

So you can see that if the rest voltage VDC happens to equal 0 (no DC offset), that phase inversion and polarity inversion will have the same result and will appear to be the same thing. But add any DC offset, and the results will be different by the amount of DC offset in the signal.
G.

I read this whole thread, and the explanation given in this post is the only explanation I can wrap my head around, the rest (that are actually on-topic) just seems like unnecessarily complicated arguing for the sake of "winning" the argument - I'd like to not have my time spent in this thread be a waste, so I'm leaving here assuming this is correct, unless there's a good reason not to. :D Is there?

Also, this:
Problem #4
phase_prob_4.jpg

The top waveform is the original. The bottom is a copy that has been shifted down the timeline. What is the degree of phase shift caused by that shift in time?

G.

seems to turn the time-shift argument on it's head - does it not?
 
I read this whole thread, and the explanation given in this post is the only explanation I can wrap my head around, the rest (that are actually on-topic) just seems like unnecessarily complicated arguing for the sake of "winning" the argument - I'd like to not have my time spent in this thread be a waste, so I'm leaving here assuming this is correct, unless there's a good reason not to. :D Is there?
It's not a matter of winning an argument, Hippo, it's a mater of actually defining phase correctly. It's just plain amazing how misunderstood of a subject it is, half of the textbooks I have seen get it wrong (this is not unusual, BTW; I have yet to see a correct description of General Relativity in a pre-grad college textbook.)

Anyway, unless you intend on being a real engineer and not just a Sears engineer, don't worry about it. 98% of the people who are into this field don't understand the difference, and they get along just fine.
seems to turn the time-shift argument on it's head - does it not?
Yes it does. All four of them do because there are no correct solutions for any of them based upon the use of time shift = phase argument. This is because it's a fallacy based upon an incorrect or incomplete understanding of just what phase is, in ALL levels of education.

G.
 
OK, here's a set of 4 problems regarding phase, phase shift and timelines. I challenge anyone to show us how to solve them using the method of shifting the wave up or down the timeline.

PROBLEM #1
phase_prob_1.jpg

This is a re-offering of the original challenge I put up that got conveniently buried a couple of pages ago. Take this graph, make a copy of it and slide the copy up or down until there is a 180° phase shift. Post the resulting two waves (the original with the phase shifted one underneath it) to this thread for your answer. Bonus: Do it again, choosing any degree of phase shift you wish (90°, 222°, whatever), and labeling the amount of phase shift as that number. This is for those that may not like 180° for some reason, or think that selecting that number is some kind of trick.

PROBLEM #2
phase_prob_2.jpg

These two waveforms show the original waveform on top (a.), and a phase inverted (180° phase change) version on the bottom (b.) (not accomplished by a polarity inversion, though the results would in this case look the same). In which direction has the waveform been slid up or down the timeline?

PROBLEM #3
phase_prob_3.jpg

How far up or down the timeline would one have to move a copy of the waveform in order to achieve a phase shift of 180° from the original? (Or 90° or 270° or whatever other amount of phase shift you wish to calculate for.)

Problem #4
phase_prob_4.jpg

The top waveform is the original. The bottom is a copy that has been shifted down the timeline. What is the degree of phase shift caused by that shift in time?

G.
From someone who is humbled and intimidated by all the math flying around -no, make that admittedly to damned lazy about some things.. :D This post is worth a thousand words.
 
It's not a matter of winning an argument, Hippo, it's a mater of actually defining phase correctly. It's just plain amazing how misunderstood of a subject it is, half of the textbooks I have seen get it wrong (this is not unusual, BTW; I have yet to see a correct description of General Relativity in a pre-grad college textbook.)
Gotcha.
Anyway, unless you intend on being a real engineer and not just a Sears engineer, don't worry about it.
lol. WTF is that supposed to mean?!
98% of the people who are into this field don't understand the difference, and they get along just fine.
Yea, I guess I fit in here - I'm doing just fine, and have no idea what anything on page two of this thread meant. My adderall gets filled on Tuesday, maybe I'll read it again, then, heh...
All four of them do because there are no correct solutions for any of them based upon the use of time shift = phase argument. This is because it's a fallacy based upon an incorrect or incomplete understanding of just what phase is, in ALL levels of education.

G.

Right, but that last one, with the little lines drawn showing that it appears to be 180 (or very close to it) at first, and then something far from 180 a little further down makes it plain as day. You should put that picture in wikipedia... :D
 
lol. WTF is that supposed to mean?!
That's a twist on the old Frank Zappa line, "Is that a real poncho or a Sears poncho?" :). I guess what it comes down to is that there are a few subjects that our hobby/vocation touches upon where the answers can be a bit more difficult than the questions, and require a decent grounding in advanced math and science topics like trigonometry, physics or information theory to truly understand the actual fundamentals behind them.

Most of us understandably simply have no interest in getting that deep into the science, don't really want to chase the engineering rabbit that deep down the rabbit hole. And, frankly, to churn out great music recordings, we really don't need to.

One doesn't really need to have a fundamental understanding of phase beyond what is normally discussed on a daily basis in these forums in order to use a stereo enhancer or holographic synthesizer. These boxes and plugs (you still here, danny.g?) that plays around with phase in very advanced ways to acheive interesting stereo and quasi-3D imaging results with our recordings. The guys that design and build those boxes need to know this stuff inside and out, but we don't need to to use them. No more than my ex-girlfriend needed to know how the turbocharger on her car worked to suck through a tank of gas every couple of days with that beast :D.

But when the question does comes up, it's not in my nature to shy away from the answer and just go with the wikiality of it. I see that as simply perpetuating the common ignorance of the subject. Most everybody dropped out of this thread after page one, and I don't blame them. We went way down the rabbit hole real quick. But that's what this subject takes, especially when bucking "conventional wisdom".

G.
 
I'm sorry, but for the nth time, the equation for a sine wave is simply sin(x). That is the VERY DEFINITION of a sine wave.

If you wish to plot it as time, as you say, the x axis itself would represent time, and there's no need to add an extra "t" variable; we already have the time value in x. The sine function is simply the change in the value of y (amplitude) over x (time).

In this case, time would be measured against cycle frequency. For example, let's say the actual frequency of the sine were f=1Hz. The peak at 90° would be at 0.25f, it would cross down over the y=0 line (180°) at 0.5 f, and so on.

I have added the graphic I promised to my previous post. Just to save everybody from having to flip back and forth between thread pages, here it is again:
phase_rotation.jpg

This shows an original reference sine wave in blue, the same sine wave rotated 90° in phase in green, and the same blue wave rotated 180° (a.k.a. "phase inverted") in orange. There is no change in the x values; i.e. no time shift involved. They are both a simple change of the phase of the original wave.

G.
The red diagram is called a lissajous and all the changes are in the X direction (time). I use these functions all the time in motion control. Our products are defined by perfect lissajous!

Salute the Lissajous!
 
The red diagram is called a lissajous and all the changes are in the X direction (time). I use these functions all the time in motion control. Our products are defined by perfect lissajous!

Salute the Lissajous!
I've always known a Lissajous curve as graphing the phase relationship between two different sines, like on an analog oscilloscope. But never mind that, we'll just confuse people even more if we get into that. And I plan on confusing enough with the rest of this post :D.

But you're right, MCI, the red part of that diagram is key. It's key to understanding phase and to the ability to shift phase without shifting time. I'm going to try and explain it a little here.

WARNING: This subject quickly pushes my graphical creation skills to their breaking point. The pictures will not be real pretty or mathematically exact in many cases, and will often be borrowed from sources on the net that I could find without spending hours searching for "just the right one". So bear with me here, gang, and try to understand the general concept at least, if not the exact details.

Phase is nothing more than a property of a waveform. Just as amplitude, frequency and duration are all properties. It's just that we are used to only looking at or graphing two of those properties at the same time; amplitude and duration (time). These are the y(vertical) and x(horizontal) axises in our DAW timelines.

(We sometimes look at amplitude and frequency in the form of an FFT spectrogram from our frequency analyzer, but that's another animal altogether. Let's stick to our DAW timeline displays.)

We use the two x and y axis to show two properties of amplitude and time simultaneously. If we want to look at a third property - such as our old friend phase - we can plot that in the third dimension, or z axis. If x is length an y is height, z would be depth.
xyz.png

On the above image, the axies have been rotated a bit to expose the z axis, but on our DAW timeline, we'd be looking the z axis head on, and it would just look like a point where the x and y axies meet.

Now, we have decided to use the third dimension, or z axis, to represent phase. But because phase is a special property mathematically equal to the 360 degrees on a circle, such a circle can be drawn (or imagined) as being on the z axis. The center of the circle is centered on the x axis (if the circle were a wheel, the x axis would be the axle).

(NOTE:, if there is DC offset, then the center would shift upwards to match the amount of offset.)

This circle, marked with its phase values in degrees, is what we see in red on this diagram:
phase_rotation.jpg

Now here's where my graphical skills fall a bit short and your imaginations have to take over for a bit to fill the gap. If we take a standard sine wave that just keeps going up and down, up and down, at a fixed frequency, what is happening is the values is actually circling around that circle at a fixed rate.

As we move through time - i.e. move down the x axis, this movement which looks like a sine wave on our 2D timeline actually looks like a spiral in the three dimensions of our "phase space" (as it would be called in math and physics). The sine wave is really little more than the 2-dimensional (amplitude and time) shadow of the spiral in the three dimensions of amplitude, time and phase.

Take a look at this photo of a typical spring, which is basically a spiral coil.
spring.jpg

Or take one out of your ball point pen there at your desk. Notice how if you look at the sping side on, it pretty much looks like a sine wave (the lower left of the picture). If you look at it edge on (through the middle, right down the x axis, with the z axis now going left-right), it just looks like a circle.

Now, we can easily take that spiral spring and spin it around. Like a drill bit, it spins around, and the lines of the 3D spiral or 2D sine wave appear to move. Yet the actual spring is not going anywhere, it is just rotating in place.

This is phase change in action. There is no shifting in time or movement along the x axis; the spring is not moving back or forth. It is simply rotating in place along the z circle, with the 2D shadow of sine wave shifting in phase as we rotate along, but without moving up or down the timeline.

G.
 
So If I wanted to cancel out a 60 cycles hum I could say make a recording, of just the hum, invert it and record my track with the hum burried in the signal, and the two should in theory negate and I will be left with just the audio signal (+ rounding errors).
 
well done dave... except that any spurious noise in either file would be amplified... and it will work only to the degree that the recordings could be time aligned... ie. to cancell tone 1 would have to be at it's peak as tone 2 is at the lowest point of the trough... make sense??
 
Yeah that does make sense, I guess the best way to get noise out of a mix is to ensure it isn't there in the first place!

I think my problem is my mic is setup next to my pc, and i am picking up fan noise or something.

I am limited atm to recording in my living room of my 1 bedroom apt. What is a good course of action to block out the noise from my PC fans? I was thinking some high density foam or the like in front of the pc, but maybe creating a sort of sound insulated portable foam wall would be a good option. Has anyone tried this?

Thanks,
Dave S.
 
I think my problem is my mic is setup next to my pc, and i am picking up fan noise or something.

I am limited atm to recording in my living room of my 1 bedroom apt. What is a good course of action to block out the noise from my PC fans? I was thinking some high density foam or the like in front of the pc, but maybe creating a sort of sound insulated portable foam wall would be a good option. Has anyone tried this?
Hey there, Dave; I'd say as the first step is to try and not have your mic next to the PC ;). If you could get your mic to the other side of the living room, pointed away from the PC, and preferably pointed towards drapes or padded furniture, to reduce the amount of fan sound reflecting off the back wall back into the mic, if possible. Yeah it may be a little of a pain to have to walk across the room every time you hit record, but you get used to such things.

You might also want to check out the studio building and the DIY forums on this BBS. One of the more recent innovations is a DIY insulated isolation box that you actually put the mic in. The iso box has one open end into which you sing or point your kazoo, or whatever instrument you play, with the other surrounding sides blocking out the rest of the room. You can make your own with materials available from your local stores very cheaply. Do a search of those forums for instructions, or maybe google "DIY microphone isolation".

The drawback to that is that you will get fairly dead sound - not a lot of natural reverb. Then again, if your room doesn't sound very good to begin with, it's not a great loss anyway. You can always add some verb to taste after you record.

HTH,

G.
 
PROBLEM #1
phase_prob_1.jpg

This is a re-offering of the original challenge I put up that got conveniently buried a couple of pages ago. Take this graph, make a copy of it and slide the copy up or down until there is a 180° phase shift. Post the resulting two waves (the original with the phase shifted one underneath it) to this thread for your answer. Bonus: Do it again, choosing any degree of phase shift you wish (90°, 222°, whatever), and labeling the amount of phase shift as that number. This is for those that may not like 180° for some reason, or think that selecting that number is some kind of trick.

Your premise is flawed that there is only one answer. There are multiple answers, each based on one term of the Fourier Series expansion for this complex wave. Please see my previous posts.

180 Degrees, or any value for that matter is nonsensical for a complex wave, but can be applied to a single term in the Fourier Series (i.e. single frequency sine wave).

Now for a sine wave of frequency w, a 180 degree shift is pi since 360 degrees is 2*pi radians/sec

Example:

Frequency is 6.28 rad/sec or 1Hz

a shift of 180 degrees or pi radians is

3.14 radians divided by 6.28 radians/sec = .5 sec

Break the wave above into it's Fourier Series expansion and then one can manipulate each term or manipulate the complex wave based on a very complex analysis of each term.

An example is making a copy of a complex wave and sliding some small time amount. The resultant wave is the sum and difference of the terms of the Fourier series (single frequencies). When recording guitars or very frequency rich sources (and by using two mics) sliding one against the other some time amount can act as a very complex EQ that you cannot garner otherwise.


PROBLEM #2
phase_prob_2.jpg

These two waveforms show the original waveform on top (a.), and a phase inverted (180° phase change) version on the bottom (b.) (not accomplished by a polarity inversion, though the results would in this case look the same). In which direction has the waveform been slid up or down the timeline?

Again, another flawed premise. This is not a phase change; it is a polarity inversion. Not the same thing.


PROBLEM #3
phase_prob_3.jpg

How far up or down the timeline would one have to move a copy of the waveform in order to achieve a phase shift of 180° from the original? (Or 90° or 270° or whatever other amount of phase shift you wish to calculate for.)

See my response to #1 and would require the addition of Unit Impulse Functions.


Problem #4
phase_prob_4.jpg

The top waveform is the original. The bottom is a copy that has been shifted down the timeline. What is the degree of phase shift caused by that shift in time?

See my response to #1 and #3.
 
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Your initial premise is flawed which is that a complex wave has a single frequency thus a single phase shift for all frequencies. There is not a single answer. There are multiple answers, each based on one term of the Fourier Series expansion for this complex wave. Please see my previous posts.
This is exactly what I have been saying all along. I have brought up the need for Fourier transforms at least twice already, going all the way back to the first page, and insisting that one cannot effect a phase change by a simple movement of the wave on the timeline. This is, in fact what started this whole to-do, if you go back and look.

BUT, what you just don't get is that the component frequencies *are not moved in time*, they are rotated in phase. Were they to be moved, each frequency would need to be moved a different amount, causing a far more radical change in the nature of the waveform than just a phase change.
180 Degrees, or any value for that matter is nonsensical for a complex wave
No, it's not nonsensical at all. Any complex wave function can be rotated by a specifically selected degree any time we want. It just can't be done along the x axis, it requires rotation around the x axis.
Now for a sine wave of frequency w, a 180 degree shift is pi since 360 degrees is 2*pi radians/sec

Example:

Frequency is 6.28 rad/sec or 1Hz

a shift of 180 degrees or pi radians is

3.14 radians divided by 6.28 radians/sec = .5 sec
And you can remove the time factor altogether and simply say that for any sine of any frequency, a rotation of 180° = 3.14 rad. This will be true regardless of frequency, and there's no need to even bring frequency into it. This is where you keep getting the mental block, sonixx; This is a step further than you need go; phase can be defined and rotated independent of frequency, and therefore can be defined and rotated independent of time.

Frequency and phase are two separate properties of any waveform, simple or complex, and can be manipulated independently of each other. Phase can be manipulated independent of frequency just as frequency can be manipulated independent of phase.
An example is making a copy of a complex wave and sliding some small time amount. The resultant wave is the sum and difference of the terms of the Fourier series (single frequencies). When recording guitars or very frequency rich sources (and by using two mics) sliding one against the other some time amount can act as a very complex EQ that you cannot garner otherwise.
Not only absolutely true, but a re-telling of what I already said earlier. It is, however, not really all that different from summing sliding two sines that are time delayed - same frequency or not - into each other, you still wind up with a third waveform that is a sum of the two out-of-phase waves, and does not resemble either of the originals. I don't see how that relates to your misunderstanding.
Again, another flawed premise. This is not a phase change; it is a polarity inversion. Not the same thing.
Wrong. Read the problem again. Although a polarity inversion would accomplish the same result, this was meant to represent a phase rotation of 180°.

OK, then, hotshot, same problem, but add a DC offset to both so that polarity cannot be used as the solution.
See answer to #1 but would require the addition of Unit Impulse Functions.
And what would the result look like? I'm asking in all honesty, sonixx, let's see the visual result of applying a convolution to it, as I admit I have not directly worked with those before (other than using someone else's IRs in a convolution reverb.)

G.
 
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I'll give you this... you're trying awfully hard. I really loved the f(t) division remark. you wouldn't believe the chuckle that one got.

I thought I was done with this but you keep writing. thanks.
 
Awww, come on, sonixx. Show me sergeant. I asked in the last post, let me ask again: And what would the result look like? I'm asking in all honesty, sonixx, let's see the visual result of applying a convolution to it, as I admit I have not directly worked with those before (other than using someone else's IRs in a convolution reverb.)

Now I'm giving you the opportunity, hotshot. Show me how Dirac convolution (or are you talking about the probability function version of the Dirac equations?) would wind up affecting the the wave, i.e. what would it look like?

And how about the inverted phase copy with DC shift applied to both waves so you can not cop out with the polarity answer, even though I stipulated aganst that in the original problem?

You're the one breaking a sweat trying to bust my chops, ace. I'm giving you the chance now. This is no time to back off. You've been trying for four years to bust me to private for some childish reason I never understood. Now's your chance.

G.
 
Define phase:

1: a particular appearance or state in a regularly recurring cycle of changes <phases of the moon>
2 a: a distinguishable part in a course, development, or cycle <the early phases of her career> b: an aspect or part (as of a problem) under consideration
3: the point or stage in a period of uniform circular motion, harmonic motion, or the periodic changes of any magnitude varying according to a simple harmonic law to which the rotation, oscillation, or variation has advanced from its standard position or assumed instant of starting
4: a homogeneous, physically distinct, and mechanically separable portion of matter present in a nonhomogeneous physicochemical system
5: an individual or subgroup distinguishably different in appearance or behavior from the norm of the group to which it belongs ; also : the distinguishing peculiarity
— pha·sic Listen to the pronunciation of phasic \ˈfā-zik\ adjective
— in phase
: in a synchronized or correlated manner
— out of phase
: in an unsynchronized manner : not in correlation

http://www.merriam-webster.com/dictionary/phase

That is from a source that is not openly editable by any old dude who can just put whatever crap they want on there (which was the argument that disqualified wikipedia, I believe)... and it seems that number 3 is the relevant definition to this discussion, right?

What is interesting is the use of the word "simple". How can the makers of the dictionary have the definition of the word so wildly incorrect? And if they are not incorrect - what is the simple harmonic law they are talking about? I mean... not to be offensive to either of the posters - but you guys are being so complicated, when the poster asked for a definition, and the very definition of the word as it applies here states that it involves a simple harmonic law. It is quite bewildering to those of us with no engineering degrees (or whatever) how the discussion of the definition has gotten this complicated.

Is it really not simple? Is the merriam-webster dictionary not a good source for the definitions of words?

Interesting thread, either way... please continue :p
 
Awww, come on, sonixx. Show me sergeant. I asked in the last post, let me ask again: And what would the result look like? I'm asking in all honesty, sonixx, let's see the visual result of applying a convolution to it, as I admit I have not directly worked with those before (other than using someone else's IRs in a convolution reverb.)

Now I'm giving you the opportunity, hotshot. Show me how Dirac convolution (or are you talking about the probability function version of the Dirac equations?) would wind up affecting the the wave, i.e. what would it look like?

And how about the inverted phase copy with DC shift applied to both waves so you can not cop out with the polarity answer, even though I stipulated aganst that in the original problem?

a Dirass equation is similar to f(t) but for Wikipedia junkies. I don't have a rats ass clue what a Dirass Equation is, but I bet you slept at a Holiday Inn Express last night.

Now on to the DC thingy...

the equation with sin(x) just for you

where x = wt

f1(x) = Vdc + a1*sin(x1) + a2*sin(x2) + a3*sin(x3) + ...

so inverted

f2(x) = -1 * f1(x)
f2(x) = -1 * (Vdc + a1*sin(x1) + a2*sin(x2) + a3*sin(x3) + ...)
f2(x) = -Vdc - a1*sin(x1) - a2*sin(x2) - a3*sin(x3) - ...

btw, f1(x) and f2(x) represent functions


You've been trying for four years to bust me to private for some childish reason I never understood.

lol, don't flatter yourself.
 
This is from the Cambridge Dictionary, which actually has an entry for "In phase/Out of phase":

If two things are happening in/out of phase they are reaching the same or related stages at the same time/at different times.
http://dictionary.cambridge.org/define.asp?key=59322&dict=CALD

It does mention time...actually the whole definition relies on time as the factor by which something is considered being in or out of phase - which totally sucks because I was so ready to accept the arguments against time having anything to do with it as presented a few posts back with pics and logical explanations and such... What a mess, heh..
 
..Go back to the drum mics example; if one ignores the transients and looks in detail at the rest of the waveform, they will, in fact, look like quite different waveforms, even though they are capturing the same source (let's pretend we're in an anechoic chamber that there is no room verb or bleed). The reason is, even though it is the same source creating just one waveform, the two mics are capturing each frequency at a different phase, bending the waveform around itself. Even if one adjusts the timeline for the delay, that alone will never bring the two waves in phase, because the phase difference is different for each frequency.
Glen, or anyone, just to ask and clarify something here. I was of the understanding that the differences in the sound at two distances was due to things like differences in frequency response/attenuation rates, radiation patterns, proximity effects, reflections and such. That with the exception those types of effects the two pass through the air for the most part with their frequency/time alignment unchanged (if that's the correct way to say that).
I did come across something IIRC about different frequencies arriving at slightly different times at extreme distances.
 
Define phase:
3: the point or stage in a period of uniform circular motion, harmonic motion, or the periodic changes of any magnitude varying according to a simple harmonic law to which the rotation, oscillation, or variation has advanced from its standard position or assumed instant of starting

The 'simple' referred to in this definition is not the same 'simple' as easy, plain and uncomplicated . . . it refers to a type of oscillation known as 'simple harmonic motion', and it is so-called, I understand, because of the deliberate exclusion of influencing factors on this motion.

Neverthless, I agree that it has been an enthralling thread, and has kept me nicely entertained.
 
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