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#1
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90 degree phase offset in CoolEdit
Hi
I am not very familiar with CoolEdit and I want to playback my voice (or any mp3 file) with a 90 degree phase offset between the 2 channels/speakers. It must be easy but how do you do this? Thanks Bob |
#2
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"Bob Pit" wrote in message
news:1110544844.814317@athnrd02 Hi I am not very familiar with CoolEdit and I want to playback my voice (or any mp3 file) with a 90 degree phase offset between the 2 channels/speakers. It must be easy but how do you do this? Effects, Filters, Graphic Phase Shifter |
#3
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In article 1110544844.814317@athnrd02, Bob Pit wrote:
Hi I am not very familiar with CoolEdit and I want to playback my voice (or any mp3 file) with a 90 degree phase offset between the 2 channels/speakers. It must be easy but how do you do this? It's not easy at all. You basically need an all-pass filter that shifts 90 degrees at all frequencies, which is not a trivial thing and it's not something any of the audio packages normally have because it's not normally very useful. Why do you want to do this? --scott -- "C'est un Nagra. C'est suisse, et tres, tres precis." |
#4
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Effects, Filters, Graphic Phase Shifter
I did a +90 degree phase shift on the left channel. It seems something like what I am looking for, but still far from it. Bob "Arny Krueger" wrote in message ... "Bob Pit" wrote in message news:1110544844.814317@athnrd02 Hi I am not very familiar with CoolEdit and I want to playback my voice (or any mp3 file) with a 90 degree phase offset between the 2 channels/speakers. It must be easy but how do you do this? Effects, Filters, Graphic Phase Shifter |
#5
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How about the "Effects, Filters, Graphic Phase Shifter" that Arny suggested?
Why do you want to do this? The reason I want it is that the effect of a voiced processed like this, is very hypnotic. I want to make hypnotic/subliminal mp3 files for myself. Bob "Scott Dorsey" wrote in message ... In article 1110544844.814317@athnrd02, Bob Pit wrote: Hi I am not very familiar with CoolEdit and I want to playback my voice (or any mp3 file) with a 90 degree phase offset between the 2 channels/speakers. It must be easy but how do you do this? It's not easy at all. You basically need an all-pass filter that shifts 90 degrees at all frequencies, which is not a trivial thing and it's not something any of the audio packages normally have because it's not normally very useful. Why do you want to do this? --scott -- "C'est un Nagra. C'est suisse, et tres, tres precis." |
#6
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Voxengo makes a phase shift plugin.
Al On Fri, 11 Mar 2005 22:42:10 +0200, "Bob Pit" wrote: Effects, Filters, Graphic Phase Shifter I did a +90 degree phase shift on the left channel. It seems something like what I am looking for, but still far from it. Bob "Arny Krueger" wrote in message ... "Bob Pit" wrote in message news:1110544844.814317@athnrd02 Hi I am not very familiar with CoolEdit and I want to playback my voice (or any mp3 file) with a 90 degree phase offset between the 2 channels/speakers. It must be easy but how do you do this? Effects, Filters, Graphic Phase Shifter |
#7
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In article 1110573659.111832@athnrd02, Bob Pit wrote:
Effects, Filters, Graphic Phase Shifter I did a +90 degree phase shift on the left channel. It seems something like what I am looking for, but still far from it. What are you looking for? --scott -- "C'est un Nagra. C'est suisse, et tres, tres precis." |
#8
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What are you looking for?
As I said, I want to make hypnotic/subliminal mp3 files for myself. The only specs I have is "90 degree phase offset". I cannot describe it in other specific ways. I can send you a very small segment of a professional created mp3 file that use this technique if you want. If you are experienced, then you will know how they did it. Bob |
#9
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In theory, a phase shift of 90 degrees is done by a capacitor.To calculate
the capacitance, for the desired frequency (20 Hz-20 kHz) you have to use the following formula:Xc= 1/(omega*c)where omega=2*pi*f, f=frequency in Hz.To give you an idea, for fm and tv frequency (VHF and UHF) we use 1nF and for AM 100 nF capacitors.So, for audio frequencies, you need a 10 micro-farad capacitor (100 times that of the AM). Tzortzakakis Dimitriïs major in electrical engineering, freelance electrician FH von Iraklion-Kreta, freiberuflicher Elektriker dimtzort AT otenet DOT gr Ï "Bob Pit" Ýãñáøå óôï ìÞíõìá news:1110544844.814317@athnrd02... Hi I am not very familiar with CoolEdit and I want to playback my voice (or any mp3 file) with a 90 degree phase offset between the 2 channels/speakers. It must be easy but how do you do this? Thanks Bob |
#10
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In article 1110576331.158713@athnrd02, Bob Pit wrote:
What are you looking for? As I said, I want to make hypnotic/subliminal mp3 files for myself. The only specs I have is "90 degree phase offset". I cannot describe it in other specific ways. I can send you a very small segment of a professional created mp3 file that use this technique if you want. If you are experienced, then you will know how they did it. No, a 90-degree phase shift is really not very audible at all. Again, it's an all-pass thing. Are you thinking about some kind of comb filtering, and not really phase shift at all? Since MP3s don't exactly preserve phase very well anyway, any of this stuff is going to be mostly lost in MP3 encoding in any event. --scott -- "C'est un Nagra. C'est suisse, et tres, tres precis." |
#11
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No, a 90-degree phase shift is really not very audible at all. Again,
it's an all-pass thing. Are you thinking about some kind of comb filtering, and not really phase shift at all? I wish I knew what these mean. If I knew all these, probably I would not ask for help in this forum. Bob |
#12
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Can you post a link to what you're talking about? It would be easier to
offer help. Thanks "Dimitrios Tzortzakakis" wrote in message ... In theory, a phase shift of 90 degrees is done by a capacitor.To calculate the capacitance, for the desired frequency (20 Hz-20 kHz) you have to use the following formula:Xc= 1/(omega*c)where omega=2*pi*f, f=frequency in Hz.To give you an idea, for fm and tv frequency (VHF and UHF) we use 1nF and for AM 100 nF capacitors.So, for audio frequencies, you need a 10 micro-farad capacitor (100 times that of the AM). Tzortzakakis Dimitriïs major in electrical engineering, freelance electrician FH von Iraklion-Kreta, freiberuflicher Elektriker dimtzort AT otenet DOT gr Ï "Bob Pit" Ýãñáøå óôï ìÞíõìá news:1110544844.814317@athnrd02... Hi I am not very familiar with CoolEdit and I want to playback my voice (or any mp3 file) with a 90 degree phase offset between the 2 channels/speakers. It must be easy but how do you do this? Thanks Bob |
#13
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"Bob Pit" wrote ...
I am not very familiar with CoolEdit and I want to playback my voice (or any mp3 file) with a 90 degree phase offset between the 2 channels/speakers. It must be easy but how do you do this? 90 degrees of phase shift depends on what frequency you are talking about, doesn't it? It is 1000x longer for 20Hz than it is for 20KHz |
#14
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"Scott Dorsey" Bob Pit : I am not very familiar with CoolEdit and I want to playback my voice (or any mp3 file) with a 90 degree phase offset between the 2 channels/speakers. It must be easy but how do you do this? It's not easy at all. You basically need an all-pass filter that shifts 90 degrees at all frequencies, which is not a trivial thing and it's not something any of the audio packages normally have because it's not normally very useful. ** Here is how you do it: http://home.att.net/~wa1sov/technica...s/allpass.html Enjoy......... Why do you want to do this? ** He is loopy. ............. Phil |
#16
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Bob Pit wrote: Hi I am not very familiar with CoolEdit and I want to playback my voice (or any mp3 file) with a 90 degree phase offset between the 2 channels/speakers. It must be easy but how do you do this? You need a filter called a Hilbert transformer. Not a thing readily available with DAW software but an FIR can be generated in Matlab which does a pretty good job and can be applied via Cool Edit's convolution function. Bob -- "Things should be described as simply as possible, but no simpler." A. Einstein |
#17
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Scott Dorsey wrote:
In article 1110544844.814317@athnrd02, Bob Pit wrote: Hi I am not very familiar with CoolEdit and I want to playback my voice (or any mp3 file) with a 90 degree phase offset between the 2 channels/speakers. It must be easy but how do you do this? It's not easy at all. You basically need an all-pass filter that shifts 90 degrees at all frequencies, which is not a trivial thing and it's not something any of the audio packages normally have because it's not normally very useful. Funny - thing is I have on occasion seen in the course of my TV Audio duties program sources that show themselves on my Tektronics scope to be 90% out of phase, but I was unaware there was anything potentially subliminal involved. g I forget exactly the details though, something to do with one side of a balanced stereo feed being half patched in the patchbay , with maybe the two sides having reversed polarity. Will Miho NY Music and TV Audio Guy Staff Audio / Fox News / M-AES "The large print giveth and the small print taketh away..." Tom Waits |
#18
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"WillStG" Funny - thing is I have on occasion seen in the course of my TV Audio duties program sources that show themselves on my Tektronics scope to be 90% out of phase, ** That could only be so with a test tone in use. .............. Phil |
#19
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I am not very familiar with CoolEdit and I want to playback my voice
(or any mp3 file) with a 90 degree phase offset between the 2 channels/speakers. It must be easy but how do you do this? You need a filter called a Hilbert transformer. Not a thing readily available with DAW software but an FIR can be generated in Matlab which does a pretty good job and can be applied via Cool Edit's convolution function. Yes, and wouldn't he also have to compensate for the delay in the Hilbert FIR by delaying the other unprocessed channel by 1/2 the length of the Hilbert FIR? Joe |
#20
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"Joseph Meditz" You need a filter called a Hilbert transformer. Not a thing readily available with DAW software but an FIR can be generated in Matlab which does a pretty good job and can be applied via Cool Edit's convolution function. Yes, and wouldn't he also have to compensate for the delay in the Hilbert FIR by delaying the other unprocessed channel by 1/2 the length of the Hilbert FIR? ** See my post on this - a Hilbert transformer delays and phase shifts both channels, one 90 degrees more than the other. Remember - the OP wanted " ... a 90 degree phase offset between the 2 channels/speakers. " ................ Phil |
#21
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"Phil Allison" "Joseph Meditz" Yes, and wouldn't he also have to compensate for the delay in the Hilbert FIR by delaying the other unprocessed channel by 1/2 the length of the Hilbert FIR? ** Forget this: " ** See my post on this - a Hilbert transformer delays and phase shifts both channels, one 90 degrees more than the other. " ** The OP will need to use the two all pass chains of the Hilbert transformer for Left and Right channels. AFAIK there is no way to produce a quadrature version of a given audio signal. .............. Phil |
#22
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Joseph Meditz wrote: I am not very familiar with CoolEdit and I want to playback my voice (or any mp3 file) with a 90 degree phase offset between the 2 channels/speakers. It must be easy but how do you do this? You need a filter called a Hilbert transformer. Not a thing readily available with DAW software but an FIR can be generated in Matlab which does a pretty good job and can be applied via Cool Edit's convolution function. Yes, and wouldn't he also have to compensate for the delay in the Hilbert FIR by delaying the other unprocessed channel by 1/2 the length of the Hilbert FIR? Yes. I'd do that by creating a stereo FIR with one channel just having a 0 dB impulse in the middle and the Hilbert transform on the other channel. If you were to mix those two channels you'd have what's called a quadrature mixer and the result would be a constant phase shift of between 0 and 90 at every frequency, the angle determined by the mix ratio. Bob -- "Things should be described as simply as possible, but no simpler." A. Einstein |
#23
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Phil Allison wrote: AFAIK there is no way to produce a quadrature version of a given audio signal. Then modify what you know. Bob -- "Things should be described as simply as possible, but no simpler." A. Einstein |
#24
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"Phil Allison" wrote in message
AFAIK there is no way to produce a quadrature version of a given audio signal. That why SSB transmitters, a popular form of which is dependent on the production of two audio signals that are in quadrature, never work. ;-) BTW, I generated a stereo test tone composed of 1 second segments of 100 Hz, 500 Hz, 1KHz, 5 KHz and 10 KHz in Audition. I then applied the 90 degree preset for the graphic phase shifter to the right channel. Each segment of the right channel of the test tone was in fact phase shifted by 90 degrees from the corresponding segment of the left channel. I conclude that since Phil is always right, my test tone composed of 1 second segments of 100 Hz, 500 Hz, 1KHz, 5 KHz and 10 KHz is in fact not a "given audio signal". What is it? ;-) |
#25
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On Fri, 11 Mar 2005 14:41:46 +0200, "Bob Pit" wrote:
I am not very familiar with CoolEdit and I want to playback my voice (or any mp3 file) with a 90 degree phase offset between the 2 channels/speakers. It must be easy but how do you do this? We need to find out just what you mean by "90 deg phase offset". You're going to get a lot of technical willy-waving now from people who'll delight in taking your request literally. But I bet that isn't what you want. Can you point us to the source that suggested "90 deg phase offset"? CubaseFAQ www.laurencepayne.co.uk/CubaseFAQ.htm "Possibly the world's least impressive web site": George Perfect |
#26
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"Arny Krueger" = autistic Yank ****wit "Phil Allison" AFAIK there is no way to produce a quadrature version of a given audio signal. That why SSB transmitters, a popular form of which is dependent on the production of two audio signals that are in quadrature, never work. ** Hey you congenital Septic Tank ****wit - go back to primary school and learn to ****ing read !!!!!!!!!! Producing two signals in phase quadrature is what a Hilbert transformer does - what I mentioned is another matter. BTW, I generated a stereo test tone composed of 1 second segments of 100 Hz, 500 Hz, 1KHz, 5 KHz and 10 KHz in Audition. I then applied the 90 degree preset for the graphic phase shifter to the right channel. Each segment of the right channel of the test tone was in fact phase shifted by 90 degrees from the corresponding segment of the left channel. I conclude that since Phil is always right, my test tone composed of 1 second segments of 100 Hz, 500 Hz, 1KHz, 5 KHz and 10 KHz is in fact not a "given audio signal". What is it? ** It ain't one ****ing bit like like he one I would give you to try. Given means " any given" ie an arbitrary signal - unlike one specially suited to the purpose. Wake up, grow up and **** the hell off. ............ Phil |
#27
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There's no link, I just read through the book electrical circuits, which is
necessary to pass to get the degree in EE in college. -- Tzortzakakis Dimitriïs major in electrical engineering, freelance electrician FH von Iraklion-Kreta, freiberuflicher Elektriker dimtzort AT otenet DOT gr Ï "Dave Kowalski" Ýãñáøå óôï ìÞíõìá ... Can you post a link to what you're talking about? It would be easier to offer help. Thanks "Dimitrios Tzortzakakis" wrote in message ... In theory, a phase shift of 90 degrees is done by a capacitor.To calculate the capacitance, for the desired frequency (20 Hz-20 kHz) you have to use the following formula:Xc= 1/(omega*c)where omega=2*pi*f, f=frequency in Hz.To give you an idea, for fm and tv frequency (VHF and UHF) we use 1nF and for AM 100 nF capacitors.So, for audio frequencies, you need a 10 micro-farad capacitor (100 times that of the AM). Tzortzakakis Dimitriïs major in electrical engineering, freelance electrician FH von Iraklion-Kreta, freiberuflicher Elektriker dimtzort AT otenet DOT gr Ï "Bob Pit" Ýãñáøå óôï ìÞíõìá news:1110544844.814317@athnrd02... Hi I am not very familiar with CoolEdit and I want to playback my voice (or any mp3 file) with a 90 degree phase offset between the 2 channels/speakers. It must be easy but how do you do this? Thanks Bob |
#28
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In article 1110579825.435618@athnrd02, Bob Pit wrote:
No, a 90-degree phase shift is really not very audible at all. Again, it's an all-pass thing. Are you thinking about some kind of comb filtering, and not really phase shift at all? I wish I knew what these mean. If I knew all these, probably I would not ask for help in this forum. Okay, comb filtering is what happens when you sum a signal that has been shifted slightly in _time_ (not phase) with the original signal. This results in a frequency response that looks like a toothed comb, and has a somewhat airy and distant sound to it. You can take a signal and shift it in _time_, in which every frequency is shifted the same time factor, or you can shift it in _phase_, in which the lower notes are shifted longer in time than the higher notes. A tape machine is designed to shift signals in time... you put signals in and what you get out is delayed by hours if not years when you play it back. A delay in _phase_ is like that, but in varying amounts for different frequencies. --scott -- "C'est un Nagra. C'est suisse, et tres, tres precis." |
#29
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Richard Crowley wrote:
"Bob Pit" wrote ... I am not very familiar with CoolEdit and I want to playback my voice (or any mp3 file) with a 90 degree phase offset between the 2 channels/speakers. It must be easy but how do you do this? 90 degrees of phase shift depends on what frequency you are talking about, doesn't it? It is 1000x longer for 20Hz than it is for 20KHz Right. That is why a filter with constant phase shift at all frequencies is very difficult to build. It's possible to do in the digital domain, but it's not very useful. --scott -- "C'est un Nagra. C'est suisse, et tres, tres precis." |
#30
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"Bob Pit" wrote in news:1110573659.111832@athnrd02:
Effects, Filters, Graphic Phase Shifter I did a +90 degree phase shift on the left channel. It seems something like what I am looking for, but still far from it. Did you try mixing the two channels to mono? Is that the effect you want? |
#31
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Right. That is why a filter with constant phase shift at all frequencies
is very difficult to build. It's possible to do in the digital domain, but it's not very useful. It is, for matrixed surround systems, or situations where you want to reduce the build-up of mono components when stereo recordings are mixed to mono. Traditionally, 90-degree phase-shift filters are implemented as an all-pass filter for the signal that is _not_ to be shifted, plus an all-pass filter that has the shift of the first filter, plus 90 degrees, for the signal that _is_ to be shifted. qv, SQ, QS, et al. |
#32
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On 3/11/05 5:24 PM, in article 1110579825.435618@athnrd02, "Bob Pit"
wrote: No, a 90-degree phase shift is really not very audible at all. Again, it's an all-pass thing. Are you thinking about some kind of comb filtering, and not really phase shift at all? I wish I knew what these mean. If I knew all these, probably I would not ask for help in this forum. Bob Hey.. Bob... Ya don;t have to know, just listen to the less-kneejerk-manic types here (like Scott!) who are still with you rather than being hyperkinetic foulmouth reactionary intellectia. (?!) Due to my self-limited time for reading this forum (I wanna help so many but the incredible amount of sheer beligerance boggles) I start skipping even the interesting threads like this when they get pointlessly whacky. Can you (if you haven;t... I might've missed it) actually DESCRIBE the effect you;re looking to achieve, maybe even an example of a recording that demonstrates it? JV |
#33
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On 3/12/05 9:18 AM, in article , "Scott Dorsey"
wrote: 90 degrees of phase shift depends on what frequency you are talking about, doesn't it? It is 1000x longer for 20Hz than it is for 20KHz Right. That is why a filter with constant phase shift at all frequencies is very difficult to build. It's possible to do in the digital domain, but it's not very useful. --scott Never thought of this... What the hell does that SOOUND LIKE? Doesn;t the old COMREX system do this... No wait, that's LINEAR frequency shifting.. Not the same thing at all. |
#34
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On 3/11/05 4:26 PM, in article 1110576331.158713@athnrd02, "Bob Pit"
wrote: What are you looking for? As I said, I want to make hypnotic/subliminal mp3 files for myself. The only specs I have is "90 degree phase offset". I cannot describe it in other specific ways. I can send you a very small segment of a professional created mp3 file that use this technique if you want. If you are experienced, then you will know how they did it. I'll make some wildassed speculation here. Possible #1: Simple reverse-polarity between left and right channels. (while this is almost always thought of as "180deg phase shift". It's only 180deg at ONE frequency... Which is why everybody MUST understand that REVERSE PHASE really means NOTHING like REVERSE POLARITY). This results (especially in headphones) in a bizarre sort of 'behind-me' effect. It also means that the sound COMPLETELY VANISHES when the audio is listened to in mono. What it might do to how various processors handle it, is up for grabs... For instance let's say you want to compress the stereo pair (which as I said are reverse=polarity) and the compressor senses the overall level at any instant by COMBINING left-and-right channels, just to derive the control signal to discern how much gain reduction to effect, then with the polarity flop in the signal, that control-signal instead of being a very real SUM of left and right overall levels, becomes ZERO and the compressor might do NOTHING or merely get 'interesting' in it's actions. POSSIBLE #2 Simple SHORT time-delay between channels. (on the order of milliseconds) This is actually phase-shift, but while the TIME might be a constant (say a few milliseconds) the amount of PHASE shifted varies with frequency, way more at hi's, very little with lo's. This again results (since it's playing with arrival-times at left-vs-right ear) in a 'where-IS-that-coming-from' effect in your head, again especially in headphones. When THIS sort of thing is summed to mono, the effect goes from a minimal vacuum-cleaner-hose hollow effect to, with time-delays on the order of 50ms on up, VERY whacked peaks and cancellations of frequencies all up and down the spectrum, mathematically related, that, when looked at on an analyser, show as regularly-spaced peaks and dips wider-and-fewer (for short delay times), through MASSIVE numbers of lines of peaks and dips closer and closer together at regular intervals, making the chart look like teeth in a comb. SUMMATION: These two are EASY to achieve with most any audio gear you have available. You might try them to see if they can do what you want to hear. You have nothing to lose (not even money!) Beyond these two approaches, you walk into the mathematical REAL world of serious weird stuff, and what the folks here have been going on (at wonderful length) about... And THAt has been a real breath of fresh air (excluding the kneejerk socially-inept inexcusable foulmouth overeactions to what SHOULD be simple pleasant exploration of a concept) amongst the mundanity. Hope this helps Jv |
#35
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Phil Allison wrote: "Phil Allison" "Joseph Meditz" Yes, and wouldn't he also have to compensate for the delay in the Hilbert FIR by delaying the other unprocessed channel by 1/2 the length of the Hilbert FIR? ** Forget this: " ** See my post on this - a Hilbert transformer delays and phase shifts both channels, one 90 degrees more than the other. " ** The OP will need to use the two all pass chains of the Hilbert transformer for Left and Right channels. AFAIK there is no way to produce a quadrature version of a given audio signal. ............. Phil A +45 and -45 degree shifted version of a given audio signal can be approximated in real time over a limited range of frequencies using a large number of RC networks. Mark |
#36
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John wrote:
On 3/12/05 9:18 AM, in article , "Scott Dorsey" wrote: 90 degrees of phase shift depends on what frequency you are talking about, doesn't it? It is 1000x longer for 20Hz than it is for 20KHz Right. That is why a filter with constant phase shift at all frequencies is very difficult to build. It's possible to do in the digital domain, but it's not very useful. Never thought of this... What the hell does that SOOUND LIKE? Doesn;t the old COMREX system do this... No wait, that's LINEAR frequency shifting.. Not the same thing at all. As Sommerwerck points out, this is how the rear channels are encoded with some of the matrix quadraphonic systems. And what it sounds like, for the most part, isn't much at all. If you listen to the things undecoded, they may sound a little "funny" but not offensively so. --scott -- "C'est un Nagra. C'est suisse, et tres, tres precis." |
#37
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On 3/12/05 4:05 PM, in article , "Scott Dorsey"
wrote: John wrote: On 3/12/05 9:18 AM, in article , "Scott Dorsey" wrote: 90 degrees of phase shift depends on what frequency you are talking about, doesn't it? It is 1000x longer for 20Hz than it is for 20KHz Right. That is why a filter with constant phase shift at all frequencies is very difficult to build. It's possible to do in the digital domain, but it's not very useful. Never thought of this... What the hell does that SOOUND LIKE? Doesn;t the old COMREX system do this... No wait, that's LINEAR frequency shifting.. Not the same thing at all. As Sommerwerck points out, this is how the rear channels are encoded with some of the matrix quadraphonic systems. And what it sounds like, for the most part, isn't much at all. If you listen to the things undecoded, they may sound a little "funny" but not offensively so. And there's where I get left behind... Wouldn't constant phase shift mean VARYING time shift across the spectrum and everything goes to hell in a handbucketbrigadedevice? |
#38
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John wrote:
And there's where I get left behind... Wouldn't constant phase shift mean VARYING time shift across the spectrum and everything goes to hell in a handbucketbrigadedevice? Right, so an impulse no longer looks like an impulse, but is sort of smushed to one side or the other. It tends to make detail sound a little bit smeary... string attacks don't sound sharp any more. Kind of an AM radio sound thing, since I guess that's where people are most familiar with massive group delay. --scott -- "C'est un Nagra. C'est suisse, et tres, tres precis." |
#39
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As Sommerwerck points out, this is how the rear channels are encoded
with some of the matrix quadraphonic systems. And what it sounds like, for the most part, isn't much at all. If you listen to the things undecoded, they may sound a little "funny," but not offensively so. When played in stereo, on speakers that image well, the rear channels of an SQ recording appear slightly "outside" the speakers. |
#40
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John wrote: And there's where I get left behind... Wouldn't constant phase shift mean VARYING time shift across the spectrum and everything goes to hell in a handbucketbrigadedevice? Yes. Think of it as a magnitude compensated first derivative of the signal WRT time. Bob -- "Things should be described as simply as possible, but no simpler." A. Einstein |
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