rePhase, loudspeaker phase linearization, EQ and FIR filtering tool

[pos]

Originally Posted by john k...

Just how long does the impulse response have to be (samples) to have any accuracy at low frequerncy?

Depends on what you want to achieve.
Give me an example of EQ, phase linearization, or linear phase filter of a given slope and frequency, and I will post some curves showing what can be expected depending on the number of taps (impulse length).

[john k...]

How about a 2nd order 20 Hz, HP with a Q=1, 6 dB boost centered at 20 Hz.

[pos]

Here goes!
This is from the rePhase interface, but it should be accurate.
Blue is target, red is result (after several automated optimization steps)

[pos]

Another test with the same EQ at different frequencies, with a 512 taps impulse:
20Hz, 40Hz, 80Hz, 160Hz, 320Hz, 640Hz

[pos]

Originally Posted by john k...

How about a 2nd order 20 Hz, HP with a Q=1, 6 dB boost centered at 20 Hz.

Just reread your post and I think I misread it the first time
Sorry about that!
What is it you want me to simulate exactly?
2nd Order Q=1 HP together with a 6dB boost?
What Q for the boost?

Or is it phase linearizion and not actual filtering that you want me to show?

[john k...]

No, what I wanted was a 2nd order high pass filter, say a B2 at 20 Hz. Then add a Q =1, +6dB boost centered at 20 Hz. So there are 2 stages. But, the plots above show the point I was getting at. You need about 8k taps at 48k sampling to get good resolution at 20 Hz. And if you go to 96k sampling you would need about 16k taps....and so fourth as the sampling rate increases. This has a dramatic effect on processing time even when using partitioned convolution.

So these high sampling rates Twest820 was asking for really aren't all that useful. The impulse would (sampling rate)/6 taps long to have reasonable accuracy at 20 Hz. You are probably going to start having problems with round off errors etc.

By the way, Merry Christmass to all.

[Barleywater]

2nd order Butterworth 20Hz high pass with 20Hz Q=1 6dB:

HP But20Hz 2nd and Para Q1 6db.gif

Zoom of IR to -132dB:

10k taps.gif

Zoom of IR to -90dB

4ktaps.gif

From above it is clear that truncation to less than 8k taps introduces questionable artifacts.

For real control of subs IR get longer.

Higher Q filters push filter length up very quickly.

Correction of LF in room swells this right up too.

I get most consistent results with 16k-32k taps.

For speaker operating >40Hz I've done quite well down to 8k taps.

Regards,

Andrew

[pos]

John, the impulse length is that much of a problem, depending on how you look at it:

- Concerning computation cost, if you are doing an active crossover you can downsample the low frequency channels, like Four Audio does in its FIR processor. No need for 96khz or even 48khz for channels that have a LP at 300Hz for example: 8khz is more than enough, and gives you 5 times the "power" for the same impulse length...

- Concerning processing delay, you can reduce it by progressively doing minimal-phase correction in the lows (again, like Four Audio does, with their mixed phase approach). You can even do the whole thing with minimal phase correction, and the impulse will extend on the right (rePhase will auto center it with the impulse peak right at the start), and their will be no delay at all (but it will still be better than the equivalent biquads regarding rounding errors)

[john k...]

I'm just looking at what we did with the Bodzio Ultimate Equalizer. I don't know what the consequences of down sampling some parts of the signal would have on fidelity and then making sure everything is synchronized, or what about the case where you are just equalizing amplitude and linearizing phase of a passive speaker. It's not really possible to down sample in that case as the signal is full range.

In any event, I'm not too sure I would want to down sample part of the signal in any event. Still, there are some instances where down sampling is not an alternative.

[pos]

Danwsampling can only be used when doing an active crossover.

Here is a short description of Four Audio's approach:
Four Audio | Inside the HD2
(see "multirate processing" section)
They have a pdf white paper that was published somewhere around 2007 and is very interesting, but I cannot find it right now.

When doing a stereo convolution yes you would not want to downsample anything (that would turn to be quite complicated as you pointed out), but you have to consider that when doing phase linearization the impulse will extend on the left of the peak, so with auto centering (in rephase) with a given impulse length you will be able to use twice that length compared to a symetrical impulse (linear phase filtering).

With the 2x6144 taps @ 48khz of the openDRC you can "lienarize" almost anything, even bassreflex phase shifts (and it does only use direct convolution for now!).

Here is an illustration, with a somewhat "exaggerated" correction:
BR at 25Hz, and LR 96dB/oct (16th order) at 80Hz, 8000Hz and 8khz (of course only the first one present any challenge, but this was done to simulate something realistic).
Blue is target, red is result.

As you can see it all turns out perfect, and the impulse "center" is automatically set a 6092 sample within the 6144 samples of the impulse.
Adding some linear phase EQ would "symetrize" part of the impulse, but most of the energy would still be on the left of the peak and auto-centring would adapt...