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#1
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90 degree phase offset in CoolEdit
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#2
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Well, yes, dispersion is another word for what we are talking about.
Group delay is the derivative of phase. Dispersion causes non-flat group delay vs frequency which is the same thing as non-linear phase vs frequency. (Note the term non-linear here means NOT STRAIGHT LINE, it does NOT refer to non-linear in the sense that the system is amplitude dependent. These are LTI systems we are discusssing LTI= (linear Time invariant) Yes you are correct, a device that has enough dispersion to create a constant phase shift at all audio frequenices is very strange. We're getting wrapped up in semantics. I'm done.... Mark |
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#3
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"Mark" writes:
Group delay is the derivative of phase. Group delay is the derivative of phase with respect to *frequency*. Frequency is the derivative of phase with respect to *time*. -- Randy Yates Sony Ericsson Mobile Communications Research Triangle Park, NC, USA , 919-472-1124 |
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#7
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#8
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#9
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(Mike Rivers) writes:
In article writes: Group delay is the derivative of phase with respect to *frequency*. Frequency is the derivative of phase with respect to *time*. Acceleration is the derivitive of *velocity* My point was two-fold: a) phase is used differently in different contexts and the "derivative" in one context gives you a completely different quantity than the derivative in the other. b) stating that A is a derivative of a function B is, generally, useless unless you state which variable the derivative is taken by. See, I have a physics book, too. If you needed a physics book to remember that, you're losing it. -- Randy Yates Sony Ericsson Mobile Communications Research Triangle Park, NC, USA , 919-472-1124 |
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#11
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In article writes: (Mike Rivers) writes: I believe that when someone says "I've shifted the left channel 90 degrees from the right channel" nearly all the time, they'll mean that they've created that phase shift at a single frequency, typically near mid-band, with some sort of a delay. I disagree. What I think they mean is that they have passed the stereo input signal through the following system: Xr --------------------------- Yr -------- Xl --------| H(w) |---------- Yl -------- where H(w) is a practical Hilbert transformer. I can show you any number of practical (and calibrated) delays that are likely to be lying around the studio ready to patch in. What's a practical (and calibrated) Hilbert transformer, who has one, and how much do they cost? I stand by my original statement. I don't suggest that this is ALWAYS the case, because in the lab (and on paper or computer) it's indeed possible to construct such a device. But considering how many people say "phase shift" and don't know what it really means, I think I'm right, at least for those who know enough to convert between frequency and time and know that 90 degrees is 1/4 of a cycle. -- I'm really Mike Rivers ) However, until the spam goes away or Hell freezes over, lots of IP addresses are blocked from this system. If you e-mail me and it bounces, use your secret decoder ring and reach me he double-m-eleven-double-zero at yahoo |
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#12
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(Mike Rivers) writes:
In article writes: (Mike Rivers) writes: I believe that when someone says "I've shifted the left channel 90 degrees from the right channel" nearly all the time, they'll mean that they've created that phase shift at a single frequency, typically near mid-band, with some sort of a delay. I disagree. What I think they mean is that they have passed the stereo input signal through the following system: Xr --------------------------- Yr -------- Xl --------| H(w) |---------- Yl -------- where H(w) is a practical Hilbert transformer. I can show you any number of practical (and calibrated) delays that are likely to be lying around the studio ready to patch in. What's a practical (and calibrated) Hilbert transformer, who has one, and how much do they cost? I stand by my original statement. I don't suggest that this is ALWAYS the case, because in the lab (and on paper or computer) it's indeed possible to construct such a device. But considering how many people say "phase shift" and don't know what it really means, I think I'm right, at least for those who know enough to convert between frequency and time and know that 90 degrees is 1/4 of a cycle. Tell you what, Mike - you just believe that and don't bother your little head about this other nonsense, OK? -- Randy Yates Sony Ericsson Mobile Communications Research Triangle Park, NC, USA , 919-472-1124 |
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#13
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#14
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#15
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(Mike Rivers) writes:
In article writes: My point was two-fold: a) phase is used differently in different contexts That was my point, too. It's used correctly in some contexts and incorrectly in others. The two contexts I was alluding to are both "correct," just different. and the "derivative" in one context gives you a completely different quantity than the derivative in the other. I assume you're talking about the mathematical derivitive, the change with respect to time. Not all "mathematical" derivatives are with respect to time, but they are all with respect to "something," i.e., some specific variable. I'm not sure of the significance of this on the practical level. Enlighten me if you can. In one context (the one we're primarily discussing here), "phase" is the phase response of a system as a function of frequency f, which I'll denote as phi(f). In this context, the derivative of phi(f) with respect to f is related to the group delay G(f), G(f) = -(1/(2*pi)) * (d phi(f) / df). Note that the units of G(f) are seconds. In another context, "phase" is the argument of a sinusoid as a function of time, which I'll denote as theta(t). For example, the sine wave x(t) = sin(2*pi*f*t + a) where f is the frequency of the sinusoid, t is time, and a is a constant, has a time-varying phase of theta(t) = 2*pi*f*t + a. The derivative of theta(t) with respect to t is the frequency of the sine wave, d theta(t) / dt = 2*pi*f, in radians per second. Note that in both contexts I'm using radians as the unit of phase rather than degrees. b) stating that A is a derivative of a function B is, generally, useless unless you state which variable the derivative is taken by. Yup, just like stating that the phase shift is 90 degrees without knowing what's 90 degrees different than what, and in the case of a non-repetitive waveform, when. The terminology is well-defined and the concepts well-understood within the discipline of electrical engineering. The term "phase shift" means the shift, or change, in phase a signal undergoes when it is processed by a linear, time-invariant system H(f). It is a function of frequency. In linear system theory you learn that phase shift does not depend on the signal but only the system, and in fact the phase shift is precisely the phase response phi(f) of the system, phi(f) = angle(H(f)), where "angle(z)" denotes the angle, in radians, of the complex number z, i.e., it is the "phi" in the polar form of the complex number z, z = r * exp(j*phi). So to say that a signal undergoes a 90 degree (or pi/2) phase shift is to say that it passes through a system which has a phase response of 90 degrees and unity magnitude at all frequencies, i.e., the transfer function H(f) = exp(sgn(f)*j*pi/2). -- Randy Yates Sony Ericsson Mobile Communications Research Triangle Park, NC, USA , 919-472-1124 |
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#16
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#17
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(Mike Rivers) writes:
In article writes: In one context (the one we're primarily discussing here), "phase" is the phase response of a system as a function of frequency f, which I'll denote as phi(f). In this context, the derivative of phi(f) with respect to f is related to the group delay G(f), What's the phase response? The phase of the output relative to the input? Hi Mike, Yes, that is correct. "Phase response" is a property of a system, not a signal. Using the notation I introduced above, the phase response of a system, phi(f), is related to the time delay T(f) of the signal through the system at frequency f by the following: T(f) = phi(f)/(2*pi*f), where T(f) is in seconds. In other words, the phase response of a system provides, indirectly, the frequency-dependent delay through the system. Oh, I give up. What you write is probably correct, and I understand your tutorials about the meaning of words, but I see no connection with practical audio systems whatsoever. No problem. Sorry if I'm failing to connect with you. Can you answer these three questions: Good questions! Let me try to answer: 1. What physical device can be used to apply a 90 degree phase shift to a complex audio signal? You can ignore anything below 20 Hz and above 20 kHz. A PC with a soundcard and some software. I don't know of a Hilbert transformer that you can buy as a single component, but that doesn't mean one couldn't be built. Let me emphasize that the phase response is a property of a *system*, NOT a signal. So if the system has a 90 degree response at all frequencies, then that characteristic is going to be imparted to ALL signals that are passed through it, complex or otherwise. In other words, you needn't consider a "complex" audio signal to validate the system - a simple sine wave sweep will do. 2. How you know you've accomplished it? (how would you measure it?) One easy way would be to connect a sine wave signal generator as an input into the system. Connect the output of the system into a scope and Y the output of the signal generator into the X input of the scope. Place the scope into X-Y mode (ala Lissajous patterns). Then at any one frequency, you should see a circle displayed on the scope because the output and input are 90 degrees apart. The geometry should remain a circle as you sweep the sine wave generator across the frequency band. 3. What change would you expect to hear as a result of this phase shift if the content was, say, human speech? Listen for yourself: http://www.uspsdata.org/OurHouse90.wav -- % Randy Yates % "I met someone who looks alot like you, %% Fuquay-Varina, NC % she does the things you do, %%% 919-577-9882 % but she is an IBM." %%%% % 'Yours Truly, 2095', *Time*, ELO http://home.earthlink.net/~yatescr |
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#18
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3. What change would you expect to hear as a result of this phase shift if the content was, say, human speech? Listen for yourself: http://www.uspsdata.org/OurHouse90.wav -- I think I heard a change in the stereo image indicating you changed the phase of one channel relative to the other, correct? Mark |
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#19
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"Randy Yates" wrote in message ... (Mike Rivers) writes: In article writes: In one context (the one we're primarily discussing here), "phase" is the phase response of a system as a function of frequency f, which I'll denote as phi(f). In this context, the derivative of phi(f) with respect to f is related to the group delay G(f), Listen for yourself: http://www.uspsdata.org/OurHouse90.wav Wow man, where did you get the MXR phaser ? ;-) DM |
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#20
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"Mark" writes:
3. What change would you expect to hear as a result of this phase shift if the content was, say, human speech? Listen for yourself: http://www.uspsdata.org/OurHouse90.wav -- I think I heard a change in the stereo image indicating you changed the phase of one channel relative to the other, correct? Yup - happens about halfway through the clip. -- % Randy Yates % "Remember the good old 1980's, when %% Fuquay-Varina, NC % things were so uncomplicated?" %%% 919-577-9882 % 'Ticket To The Moon' %%%% % *Time*, Electric Light Orchestra http://home.earthlink.net/~yatescr |
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#21
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"David Morgan \(MAMS\)" writes:
"Randy Yates" wrote in message ... (Mike Rivers) writes: In article writes: In one context (the one we're primarily discussing here), "phase" is the phase response of a system as a function of frequency f, which I'll denote as phi(f). In this context, the derivative of phi(f) with respect to f is related to the group delay G(f), Listen for yourself: http://www.uspsdata.org/OurHouse90.wav Wow man, where did you get the MXR phaser ? ;-) Ha! Is that what it was? Funny, I thought it was Adobe Audition!  -- % Randy Yates % "Though you ride on the wheels of tomorrow, %% Fuquay-Varina, NC % you still wander the fields of your %%% 919-577-9882 % sorrow." %%%% % '21st Century Man', *Time*, ELO http://home.earthlink.net/~yatescr |
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#22
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In article writes: "Phase response" is a property of a system, not a signal. Exactly - so you can't talk about it in isolation. But a "system" can be two signals generated by one or more black boxes. In other words, the phase response of a system provides, indirectly, the frequency-dependent delay through the system. Right. This is what I've always described as "group delay", the group being the entire collection of frequencies within the waveform. There is no single number because, as you say, each frequency gets its own little delay unit in the big black box model. I could have been using the term incorrectly all my life (which probably is a total of about five times in more than 40 years of engineering). If "group delay" is the length of time between when the leader of the pack goes in to when it comes out, that's just plain "delay" in my book. 1. What physical device can be used to apply a 90 degree phase shift to a complex audio signal? You can ignore anything below 20 Hz and above 20 kHz. Let me emphasize that the phase response is a property of a *system*, NOT a signal. So if the system has a 90 degree response at all frequencies, then that characteristic is going to be imparted to ALL signals that are passed through it, complex or otherwise. In other words, you needn't consider a "complex" audio signal to validate the system - a simple sine wave sweep will do. A "simple sine wave sweep" isn't a simple waveform. A series of sine waves that remain stable long enough to ignore the start/stop effects would suffice. If you could put in 1 kHz and get it out .25 msec later (ignoring the fact that you can't tell one cycle from another and might have 90 + multiples of 360 degree phase sheift), then put in a 2 kHz sine wave and get it out .125 msec later, that would be a start. 2. How you know you've accomplished it? (how would you measure it?) One easy way would be to connect a sine wave signal generator as an input into the system. Connect the output of the system into a scope and Y the output of the signal generator into the X input of the scope. Place the scope into X-Y mode (ala Lissajous patterns). Then at any one frequency, you should see a circle displayed on the scope because the output and input are 90 degrees apart. The geometry should remain a circle as you sweep the sine wave generator across the frequency band. That'll do it. 3. What change would you expect to hear as a result of this phase shift if the content was, say, human speech? Listen for yourself: http://www.uspsdata.org/OurHouse90.wav Not knowing what the original sounded like, it's hard to guess the change, but thanks for the example. It sounds a bit like incoherent stereo, which the original may well have been considering the era of the recording. Did you do this with a math program? -- I'm really Mike Rivers ) However, until the spam goes away or Hell freezes over, lots of IP addresses are blocked from this system. If you e-mail me and it bounces, use your secret decoder ring and reach me he double-m-eleven-double-zero at yahoo |
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#23
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Mike Rivers wrote: Not knowing what the original sounded like, it's hard to guess the change, but thanks for the example. It sounds a bit like incoherent stereo, which the original may well have been considering the era of the recording. Did you do this with a math program? Mike, here is an 8k, 32 bit float Hilbert transformer as generated by the hilbert() function of Matlab. If you have any DAW with convolution, it can be convolved with a stereo signal to hear the effect. Bob -- "Things should be described as simply as possible, but no simpler." A. Einstein |
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#24
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Bob Cain wrote: Mike Rivers wrote: Not knowing what the original sounded like, it's hard to guess the change, but thanks for the example. It sounds a bit like incoherent stereo, which the original may well have been considering the era of the recording. Did you do this with a math program? Mike, here is an 8k, 32 bit float Hilbert transformer 'Where is "here"', you may well ask. Sorry, I was in a hurry to get out the door and forgot the link: http://www.arcanemethods.com/Hilbert.wav Note that this filter has a fixed 4096 sample delay plus the 90 degree phase shift at all frequencies. It is not accurate at the extremal low frequencies and the extremal high frequencies and that is a consequence of it being a finite length approximation to the real thing. Bob -- "Things should be described as simply as possible, but no simpler." A. Einstein |
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#26
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Mike Rivers wrote: Thanks for the effort. Bob, but I have just the faintest clue about what you're talking. I have no idea what to do with whatever it is, wherever it is. Hopefully it will be useful to someone with the right smarts and software. If you have Adobe Audition, for example, there is a builtin convolution function (or plugin.) In Audition you open the ..wav file that contains the filter, invoke the convolution function, and tell it to load the active file into itself and then exit the function. You can then convolve that filter against any other files you want to by reinvoking the convolution function and telling it to convolve whatever is loaded into it with whatever the currently active file is. This is one way of employing filters that aren't native to the app, such as the Hilbert transform I linked to. If you have a way of generating the finite impulse response of any filter, you can load it into the convolution function and use that to filter audio files. Not sure if this helps any but... Bob -- "Things should be described as simply as possible, but no simpler." A. Einstein |
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#27
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Bob Cain wrote:
Mike Rivers wrote: Thanks for the effort. Bob, but I have just the faintest clue about what you're talking. I have no idea what to do with whatever it is, wherever it is. Hopefully it will be useful to someone with the right smarts and software. If you have Adobe Audition, for example, there is a builtin convolution function (or plugin.) ...snip.. You can also use Acoustic Mirror in Sound Forge... Later... Ron Capik -- PS: Was that a transform of an impulse or of a bandwidth limited impulse? |
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#28
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Ron Capik wrote: Bob Cain wrote: If you have Adobe Audition, for example, there is a builtin convolution function (or plugin.) ...snip.. You can also use Acoustic Mirror in Sound Forge... Right. Later... Ron Capik -- PS: Was that a transform of an impulse or of a bandwidth limited impulse? The input to hilbert() was one 0 dB sample with 8192 points requested as output. The bandwidth of the signal to be sampled and transformed should be limited, as usual, to fs/2. Bob -- "Things should be described as simply as possible, but no simpler." A. Einstein |
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#29
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