Once upon a time   2 comments

I got asked a question regarding how i find the frequency points and bandwidth for implementing Allpass filters when correcting phase on a driver.

To be honest i had a rough idea but most of the time i didn’t get the chance of verifying if that would work. I just started messing with putting in time offsets and kind of guessulating (? 😉 ) frequency points and bandwidth numbers to get a phase flat respons. I wish i could have done this “research” sooner but that’s live: to many things to do and not enough time……

There’s a lot of stuff on the WWW regarding phase but to me the best definition of phase would be the one i got during the first seminar from Meyer Sound back in 2005 taught by MAGU (Mauricio Ramirez).

Phase is the conversion of time or distance related to “a” frequency expressed in degrees.

It took me a “while” to get comfortable with this definition and to fully understand it let alone making sense of the phase display with this definition in mind. To put this definition in to a real world explanation: if the phase trace of a device under test goes flat  al frequencies reach the measurement point at the same time at that frequency range. By “the phase trace going flat” i mean the trace goes horizontal. This can happen at the 0º line or at other values.

Working with Smaart V8 means you have to synchronize the reference signal (pink noise/music/swept-sine wave) to a measurement signal which also opens the opportunity to put the measurement signal before the reference signal by implementing a small delay on the device under test and after synchronizing smaart to that point in time decrease the delay value (the same thing happens when moving the mic towards a loudspeaker you’re trying to measure). By doing so the phase trace goes up indicating the frequencies where the phase trace goes up are ahead in time compared to the time found by the delay finder via the live impulse respons.

First let’s take a look at “pure delay” using Smaart 8.

This screen capture is a bit edited so you can see the phase display and it’s derivative group delay in the bottom window and the effect delay has on both.

You can see the processor latency (Apex intelli-x2) 2.81ms. If i add delay in steps of 1ms the phase trace shows 360º of phase shift at 1ms delay at 1kHz 720º of phase shift at 2ms delay at 1kHz and so on.

After i reach 5ms of delay (1800º of phase shift up to 1kHz) i re-synchronized Smaart so the delay time found is 7.81ms. After that i decreased the delay also with 1ms steps and now the phase trace shows the same thing only in negative numbers.

What is important about it:

*adding delay causes the phase trace to go down and increasing delay means the angel in which the phase trace goes down steepens the angle down.

*decreasing delay causes the phase trace to go up and the more the delay is decreased the steeper the angle of the phase trace becomes.

Now let’s take a look at

*first a 4th order Linkwitz-Riley low pass filter at 1kHz.

*second a 4th order Linkwitz-Riley high pass filter at 1kHz.

*third a 2nd order allpass filter at 1kHz with a bandwidth of 2octaves.

On each filter you’ll see the phase respons first and after that the group delay.

1st The 4th order Linkwitz-Riley low pass filter at 1kHz shows the Impuls Respons moves to the right has a wider span and seems to loose a lot of “level” (I’m not going in to the why but there’s a lot less data points so level goes down).

Since the IR moves to the right you can assume all frequencies are late! and it’s stretched over a wider area. Welcome to analyzer world.

2nd I took a look at a Linkwitz-Riley 4th order high-pass filter. You can see the large spike followed by a bump. The bump is caused by the frequencies on the left side of the magnitude window. Phase goes down so those are delayed by the LR4th order filter i.e. group delay.

3rd The 2nd order allpass filter shows all frequencies passing but the timing of the frequencies in the area where the filter is implemented has changed. Again group delay at work here. The frequencies where the phase goes down are the ones seen in the IR in the bump next to the peak on the right side of the IR.

Before i go to the final screen capture (me messing about with phase respons) i have to show a catch to working with 2nd order Allpass filters.

In the screen capture I implement a 2nd order Allpass filter and play around with bandwidth. With a 2 oct. BW you see the filter influents all frequencies on the left hence group delay still has it’s effect all the way down the frequency scale. As soon as i decrease bandwidth the frequencies on the left are less effected by group delay but at the frequency you implement the 2nd order allpass filter group delay rises.

In the next screen capture  you see me working from 20kHz down to the x-over of the high driver. The reason for this is simpel: 2nd order allpass filters with a wider bandwidth effect not only the frequency point where they are implemented but also the surrounding area.

Before i realized this i always seemed to have some real problems in getting the phase trace roughly around the centre of the phase pane because i started at the x-over frequency and worked my way up the scale.

As soon as i started working from right to left (thanxs at Bob mcCarthy 606 for explaining the group delay formula in his book “the green bible” of system alignment) i gained a bit more control on where the phase trace ended up: hopefully somewhere around the 0º line centered in the middle of the phase pane.

So enjoy some pink stuff and i hope this helps a bit

Sorry for any grammar mistakes (i’m dutch and can’t help it;-) ) I’ll keep working on explaining how i work with this sh*t…..

added another screen capture.

And the data from Smaart V8.


enjoy 😉

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