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Author Topic: Temporal EQ  (Read 2861 times)

Brandon Wright

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Temporal EQ
« on: July 23, 2014, 04:14:22 pm »

In the interest of my own edification, I have been working through a lot of information on some of the finer points of complex speaker processing. Obviously, this would not be complete without working through Dave Gunness's white papers and patents on the Fulcrum site. At this point I feel that I have a pretty good idea of what is approachable and what isn't with "pre-conditioning." What I don't feel like I have a good handle on is how the transient distortion is being mitigated. How are corrections being made electronically for physical anomalies with out affecting the large portion of the energy that is directly propagated?   

It seems like the answer solely lies in the ability to correctly implement FIR filters based on the long list of qualified processors for the Level 1 presets. However, the following quote from Fulcrum's website is making me question my understanding:

"If however we supply a delayed and modified version of the original signal to the compression driver, then we can mimic the sound pressure that would occur if the compression driver were absorptive. If we do this precisely enough the compression driver diaphragm will have the same velocity that the air molecules would have had when they encountered an absorptive boundary. The sound pressure at the diaphragm will be the same as it would have been at an absorptive boundary. In fact, to the reflected wave, there is no difference between the compression driver and an absorptive boundary. In both cases, the returned wave is absorbed and the resonance is eliminated."

This sounds like active cancellation? 

Anyone want to weigh in?
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Frank Koenig

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Re: Temporal EQ
« Reply #1 on: July 23, 2014, 11:58:02 pm »

A good starting point in these discussions is to be clear whether we are talking about linear or nonlinear distortions. By linear distortion we mean distortions of the response relative to the excitation that can occur in linear systems.

If x is the excitation and y is the response, such that y = F(x), then the system F is linear if and only if  F(c1 x1 + c2 x2) = c1 F(x1) + c2 F(x2) for all c and x. In audio engineering we recognize such systems as ones that do not generate any frequencies in the output that were not present in the input.

A (single-input, single output) linear system, and its distortions, are completely characterized by the (complete) impulse response or the (complete, complex) frequency response, which are related by the Laplace transform in the case of continuous-time systems or the Z transform in the case of discrete-time systems. The Fourier and discrete Fourier transforms are special cases of wide applicability.

In so far as "temporal EQ" corrects only linear distortion, which we expect since it is implemented using linear filters, it corrects features of the system that are completely characterized by the frequency (or impulse) response and the corrections are themselves so characterized. It doesn't matter if the distortion is due to an echo or a resonance or some other physical phenomenon. If it's linear, it's there in the frequency response.

"Transient distortion" assuming it's linear, is just another bunch of wiggles in the frequency response. I avoid the term preferring something like frequency response anomalies, mostly at high frequencies.

Loudspeakers are single-input and quasi-infinite output, in that their response is different at every angle in the far field. (There probably exists some finite sampling of the response over angle that is sufficient to characterize the speaker, but that's another story.) The art in all this is identifying and correcting those frequency response (or impulse response) anomalies that are common across a large number of angles, unit-to-unit variation, and are, most importantly, perceptually significant. Dave appears to have cracked a good part of this nut and I, like you, wish I knew more about it.

As for FIR or IIR implementation, which came up in another recent post, I'll  make the following observations. IIR filters, other than a limited class of all-pass filters, are generally minimum phase and this is a good thing as most of the frequency response anomalies of speakers are also minimum phase so, as anyone who's goofed around with an equalizer has observed, fixing the magnitude with, say, an IIR bi-quad, also fixes the phase.

FIR filters have certain advantages in certain situations. Here's my current list.

They are easy to generate automatically for approximate, high-order minimum phase corrections. In this case they have no more processing delay than an IIR implementation.

They can be used to implement general, high-order all-pass filters. These exact a processing delay depending on frequency.

They can be used to implement constant delay high- and low-pass filters for crossover networks which have the advantage that there is no gross pattern shift in the crossover range resulting from non-coincident drivers. These are only useful at higher frequencies because of the processing delay.

--Frank
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Brandon Wright

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Re: Temporal EQ
« Reply #2 on: July 24, 2014, 12:29:45 pm »

Thanks Frank,

That is my understanding as well. It is the utilization of FIR to quickly, with some automation, fit an inverse of the FR for linear, roughly invariant (LTI) anomalies that remove excess excitation. 

I'm not sure then if that paragraph from Fulcrum's website is just awkward marketing or foreshadowing on the part of DG. Even more likely: I currently lack the capacity to comprehend it. 
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Arthur Skudra

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Re: Temporal EQ
« Reply #3 on: July 24, 2014, 03:48:38 pm »

Thanks Frank,

That is my understanding as well. It is the utilization of FIR to quickly, with some automation, fit an inverse of the FR for linear, roughly invariant (LTI) anomalies that remove excess excitation. 

I'm not sure then if that paragraph from Fulcrum's website is just awkward marketing or foreshadowing on the part of DG. Even more likely: I currently lack the capacity to comprehend it.
Dave has written some excellent papers on the topic while he was at EAW, take a look and download his technical papers found here:
http://fulcrum-acoustic.com/technologies/whitepapers.html

Particularly the one "Improving Loudspeaker Transient Response with Digital Signal Processing" and the matching patent document.
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Brandon Wright

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Re: Temporal EQ
« Reply #4 on: July 24, 2014, 04:21:51 pm »

Dave has written some excellent papers on the topic while he was at EAW, take a look and download his technical papers found here:
http://fulcrum-acoustic.com/technologies/whitepapers.html

Particularly the one "Improving Loudspeaker Transient Response with Digital Signal Processing" and the matching patent document.

Yep, I have read both several times now like I mentioned in the OP. My question addresses the disparity (at least what I feel is a disparity) from those readings and the Temporal EQ explained page of Fulcrum's website.
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Arthur Skudra

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Re: Temporal EQ
« Reply #5 on: July 24, 2014, 05:43:13 pm »

Yep, I have read both several times now like I mentioned in the OP. My question addresses the disparity (at least what I feel is a disparity) from those readings and the Temporal EQ explained page of Fulcrum's website.
No disparity between the papers, just that David figured out a different approach of doing things now that he is no longer with EAW where he originated his patent from.  In simple English, he figured out the math algorithms to "cancel" out the reflections in a horn (since the dimensions and geometry are finite), and created a FIR filter to do the work in DSP.
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Frank Koenig

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Re: Temporal EQ
« Reply #6 on: July 24, 2014, 05:56:35 pm »

Here's another little factoid regarding echos or reflections that I wanted to mention but had to check first that I have it right.

An ideal single echo, that is one that returns an attenuated copy of the original once, can be modeled as a minimum phase FIR filter with two non-zero coefficients. It can be compensated exactly by a minimum phase IIR filter with two non-zero coefficients.
 
An ideal multiple echo, that is one that returns an infinite sequence of exponentially decaying copies of the original, can be modeled as a minimum phase IIR filter with two non-zero coefficients. It can be compensated exactly by a minimum phase FIR filter with two non-zero coefficients.

In both cases the order of the filters is the number of samples by which the echo is delayed. You're not going to be able to use this to design a practical echo canceler, but it might be a useful conceptual starting point. It's an example of a physical process resembling a non-recursive system that can be compensated by a recursive system, and vice versa. -F
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Re: Temporal EQ
« Reply #6 on: July 24, 2014, 05:56:35 pm »


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