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Author Topic: Polar Phase Representation  (Read 1511 times)

Frank Koenig

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Polar Phase Representation
« on: April 05, 2019, 12:47:46 pm »

Last night I was reading a Motu users' manual online for some stupid reason and ran across a description of a phase representation provided by a program that's included when you buy the box. Somewhat intrigued and with nothing better to do I coded it up in R to play with. I'm not sure how useful it really is but it does have some nice properties in that it implicitly unwraps phase and, unlike a conventional unwrapped phase plot, does not require a scale change to display an arbitrarily large total phase variation.

This is a polar plot with radius representing frequency and angle representing phase (directly). You can picture it as taking a conventional (principal value) phase plot and rolling it into a cylinder by joining the top and bottom edges. Now look down the axis of the cylinder from the high-frequency end to see the plot in perspective receding into the distance. You can as well plot frequency from the outside-in, which appears as viewing the cylinder from the other end.

I tried both log and linear frequency scales. Motu's app uses log frequency but in my brief fooling around I found the linear scale more revealing. Obviously it's not hard to generate one or the other. Another tool in the box.

--Frank



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Dave Garoutte

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Re: Polar Phase Representation
« Reply #1 on: April 05, 2019, 01:04:09 pm »

Sheesh, I was just getting used to reading the standard plots and now this??!! :o
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Frank Koenig

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Re: Polar Phase Representation
« Reply #2 on: April 05, 2019, 02:50:25 pm »

Here's the same measurement plotted with log frequency scale from the outside-in. The outermost ring is 200 Hz and the center is 10 kHz with 1/2 octave per ring. The second plot is a .4 ms pure delay, for reference. I think I'm liking the outside-to-inside log-f representation. I need to play more. -F




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Russell Ault

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Re: Polar Phase Representation
« Reply #3 on: April 05, 2019, 03:37:08 pm »

Just for reference, what would a flat phase response look like in polarity and out of polarity?

-Russ
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Frank Koenig

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Re: Polar Phase Representation
« Reply #4 on: April 05, 2019, 03:49:32 pm »

Just for reference, what would a flat phase response look like in polarity and out of polarity?

-Russ

That's easy 8)  A "straight wire" would be represented as a radial line from the right edge to the origin. A straight wire with inverted polarity would be represented as a radial line from the left edge to the origin. 0 and 180 deg over all frequencies, respectively. A Hilbert transformer would be represented as a radial line from the top to the origin (90 deg). -F
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Dave Garoutte

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Re: Polar Phase Representation
« Reply #5 on: April 05, 2019, 04:00:47 pm »

That's easy 8)  A "straight wire" would be represented as a radial line from the right edge to the origin. A straight wire with inverted polarity would be represented as a radial line from the left edge to the origin. 0 and 180 deg over all frequencies, respectively. A Hilbert transformer would be represented as a radial line from the top to the origin (90 deg). -F

Cool.

Imagine having a live feed of this in your SMAART rig and the weird looks you'd get from the guest BE!
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Frank Koenig

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Re: Polar Phase Representation
« Reply #6 on: April 05, 2019, 04:36:01 pm »

Cool.

Imagine having a live feed of this in your SMAART rig and the weird looks you'd get from the guest BE!

Look at page 67 of this Motu manual. That's what got me started on this.

http://cdn-data.motu.com/manuals/firewire-usb-audio/8pre_USB_Manual_Win.pdf

It's not a replacement for Smaart, etc., but it does appear to have some interesting functionality. It's more of an oscilloscope. So you could use it to mess with your BE's brain. And the whole package, including the 8 channel USB interface, costs less than a Smaart license.

--Frank
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Barry Singleton

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Re: Polar Phase Representation
« Reply #7 on: April 05, 2019, 04:46:07 pm »

  So we have caught up with Harry Nyquist of Bell Labs I see.

  Search Nyquist Plot

  Take that into 3D and search Heiser Spiral if you want to bend your brain. Only available in TEF I believe.

  Barry.
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Frank Koenig

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Re: Polar Phase Representation
« Reply #8 on: April 05, 2019, 05:09:45 pm »

  So we have caught up with Harry Nyquist of Bell Labs I see.

  Search Nyquist Plot

  Take that into 3D and search Heiser Spiral if you want to bend your brain. Only available in TEF I believe.

  Barry.

Not quite. (I would never assume to have caught up with Nyquist.) A Nyquist plot is a projection along the frequency axis of the complex frequency response in polar form. It includes magnitude information. The Heyser spiral (note spelling) is a 3-D plot of a real signal (of time) and its analytic signal counterpart, as would be generated by a Hilbert transform, versus time.

The current representation is neither. It's just another way of plotting phase versus frequency.

--Frank

Here's a Nyquist plot of the same data. Cool looking but would need tick marks for frequency along the curve to make it meaningful.






« Last Edit: April 05, 2019, 05:48:10 pm by Frank Koenig »
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Frank Koenig

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Re: Polar Phase Representation
« Reply #9 on: April 06, 2019, 12:46:14 pm »

I hadn't thought about Nyquist diagrams in a very long time (thanks Barry) -- maybe since that undergrad classical controls class -- and never in the context of audio. They are fascinating in the forms that they take. In a few examples I ran (16 ms windowed pseudo-anechoic responses of speakers) they all appear as a sequence of arcs connected at sharp inflection points, some arcs taking more than a full circle. The log-magnitude and phase when plotted conventionally look like entirely ordinary sequences of wiggles, with the phase vaguely approximating the derivative of the log-magnitude. So what are these arcs and inflection points telling us, if anything?

I added frequency markers to the previous plot. If nothing else I keep learning more about graphing in R.

--Frank


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Re: Polar Phase Representation
« Reply #9 on: April 06, 2019, 12:46:14 pm »


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