Digital Signal Processing - How it affects phase and time domain

The graph shows the original spk+room IR as blue, The correction filter (which is indeed a reverse of the original IR) as red, and the result of correction as yellow. The closer the peak of correction is to the middle of the correcting filter, the lower ||err|| will be, if everything else is the same.

I apologize for the pathetic explanations, it is easier for me to do things than to explain how and why I've done it.

Let me show a less abstract example, and I hope it will help. Let's take a planar tweeter (AMT-920), and measure it in a room from 0.5m. Then, could we prefilter the signal in DSP by an FIR so that on the output it behaves as its idealized version? Yes, almost. a picture is better than a thousand words:
View attachment 1338997
View attachment 1338998
View attachment 1338999
Here you can see that giving ample lookahead to IR inversion allows for longer but lower pre-echo (-110 dB) and some room echo dereverberation.
The last picture may also explain why Dirac is a scam. It's a lot of noise about nothing, totally ignoring the fact that an ear is not an omni.

The code is 20 lines... but I am afraid they are cryptic to the uninitiated.

Glad to see some continuing activity in this thread, as I'm very interested in what you've done too.
Please correct observations I've made, as I try to replicate your results with the more limited tool set I have for FIR generation.

First, it looks like from the linear scale impulse responses, that your desired & corrected target curve for the AMT-920 is IIR/minimum phase.
So you're using FIR to replicate IIR? Correct?
That would make sense to me, considering I think you are showing this example as a proxy for a full-range "system example", in which case I know we would not want a linear phase high-pass filter.

What is the high-pass target...looks like maybe a higher order Bessel?
And what is the low-pass target? It's so steep I'm thinking it almost has to be linear-phase???
Do you have a handy phase plot of the corrected results?

Thx, that info will help me continue to experiment along with trying to improve ETC curves for the same type example.
 
1) So you're using FIR to replicate IIR? Correct?
Yes.
2) ..we would not want a linear phase high-pass filter.
Correct, Theoretically, we can use it but practically, AFAIK, there are no benefits to using a symmetric FIR. Using traditional LR4 or minimum-phase FIR appears preferable. Keep in mind that DSP implementations of IIRs tend to suffer from many numerical problems; we have to convert an IIR to a cascade of low-order state-space sections, etc. It took Sirrus Logic about 10 years to finally produce good anti-aliasing IIR filters.
3) What is the high-pass target...looks like maybe a higher order Bessel?
first order, it matches - more or less - the driver without non-idealities
4) And what is the low-pass target? It's so steep I'm thinking it almost has to be linear-phase???
It's a 4th order Butterworth. it matches - more or less - the driver without non-idealities
5) Do you have a handy phase plot of the corrected results?
No, I don't. Matlab's phase plots are of questionable value.
 
Thanks for all that. I should have seen first order matches, but the FIR generator i was using starts with 2nd order (made for live sound).
And can see the fourth order Butterworth fits well too.

Here's the kind of ETC I can get from a B&C dcx464 coax CD, using the HF section as my proxy for a speaker system.
With an IIR high-pass target, faintly seen as blue under the green magnitude trace.

So in comparison, your proxy speaker ETC look awesome to me !!

(I do have a lot of in-room noise no way to get rid of)

1722630530436.png


I do really like linear-phase xovers....particularly steep ones, like 96dB/oct. Probably because all my builds are usually 5-ways, and the steep filters give so much latitude in choosing crossover frequencies that stay within drivers' regions of relatively flat response. I've found relatively little impulse inversion is required to correct the meat of a drivers passband vs out of band. And the linear-phase portion of the FIR filter is then dominated by just the crossover.
Which for me means, any pre-ring is mainly due to lack of acoustic complementary from off-axis lobing.
(I personally can't imagine giving up lin-phase crossovers
 
Tangential to the subject at hand, in 2004 Peter Craven wrote a paper about apodizing filters designed to reduce pre-ring and shorten impulse response. https://secure.aes.org/forum/pubs/journal/?elib=12992
Unfortunately his technique requires a reduction in high frequency bandwidth, but the general concept may be enlightening.

Yes, in the context of ADC decimation and DAC interpolation filters. Basically a predecessor of his MQA work, but without licensing costs or lossy compression. I don't hear any difference between the steep and apodizing filters I put in my DAC, but that could very well say more about my hearing than about the concept. It's certainly interesting.