The importance of crossover steepness

[CopperTop]

Just a question about the ideas behind active crossovers.

From what I understand, a steep crossover is desirable for reasons of relieving the drivers from being driven by 'unsuitable' frequencies, and also to eliminate multipath phase cancellation/addition from two drivers being driven simultaneously and the listener being off-axis.

In my setup I am driving a pair of sacrificial Mission 702e two way speakers with a home-brew PC-based crossover configured as follows:

FFT-based linear phase filtering
FFT size: 32768
Crossover frequency: 2-9kHz selectable.
Crossover width: 50-1000 Hz selectable.
Crossover filter characteristic: linear attenuation from unity to zero over the selected crossover width

I haven't done any 'voicing' of the setup as such, merely setting the amps to give equal levels from woofer and tweeter at 3kHz, and noting that for these particular drive units they seem more-or-less in phase over the crossover region at sensible frequencies. It sounds strikingly good 'out of the box' - in some ways the best hi fi I've ever heard. I have a calibration mic ready (no anechoic chamber unfortunately!), but I am not expecting to be able to make any great improvements, and probably it'll make it worse...

I can change the crossover frequency and width in real time (rough and ready GUI screenshot enclosed).

What I find is that I can hear the effect of the cutoff frequency fairly readily, certainly at the extremes, but I have to say that I cannot hear any effect whatsoever from the crossover width. Zero. I know that, in theory, the steep crossover gives more pre- (and post-) ringing but I have yet to hear it at all. Similarly, I know that the shallower crossover should cause multi-path effects if I move up and down in relation to the speakers while listening, but again I can hear no difference whatsoever!

How audibly significant have other active crossover users found the steepness to be?

[sreten]

Hi,

"Crossover filter characteristic: linear attenuation from unity to zero over the selected crossover width"

I have no idea what that means, unity to zero over any bandwidth implies
infinite order crossover slopes and that is simply not the way it works.

rgds, sreten.

All high order slopes sound similar, the crux is low order slopes.

[kevinkr]

Any filter slope achieved by this implementation looks like high Q to very high Q based on the width of the transition region available.

[CopperTop]

Originally Posted by sreten

Hi,

"Crossover filter characteristic: linear attenuation from unity to zero over the selected crossover width"

I have no idea what that means, unity to zero over any bandwidth implies
infinite order crossover slopes and that is simply not the way it works.

Of course I'm probably dabbling with powers that are beyond my comprehension (more than likely!), but with FIR filters, is there any advantage to emulating analogue-style filter 'orders' or dB-per-octave slopes etc.? As far as I can work out, you can have pretty much any response you want, limited by the size of the FFT, and linear crossover slopes are easiest to compute! The response won't be zero outside the pass band, but it will be close with a large FFT. However, I have a nagging suspicion that there may be subtle issues that I'm missing... but I can obviously 'dial in' any desired filter response you might suggest.

All high order slopes sound similar, the crux is low order slopes.

And the advantage of low order slopes is..?

[CopperTop]

Originally Posted by kevinkr

Any filter slope achieved by this implementation looks like high Q to very high Q based on the width of the transition region available.

Ah, so a linear transition over 1000Hz would still be considered a steep crossover? Is that a problem, or a good thing?

[chaparK]

I guess this is your own application. Congrats, nice job!

My understanding of what you're doing is that you're performing a convolution of the input with successively one low-pass and one high pass. You obtained the impulse response of these filters (the 2 syncs) by computing the inverse Fourier transform of a brick-wall filter.

There's nothing wrong with this approach.

What's not clear is your concept of crossover width. Let me try to develop this.
When you compute the filters, you find out that you must truncate (or window) the theoretic impulse response otherwise you're getting an infinite number of coefficients.

From that point on, what's going to determine the steepness of the implemented filter is the number of coefficients you're effectively using. Basically the more coefficients you use, the steeper your filter.

Now when you associate a low-pass and a high-pass in a system, you have probably defined a dependency between these filters. One typical dependency is to require constant (or flat) output of the summed response Low-pass + High-pass.

From this point on, if you set the number of coefficients and the 'cut-off' frequency for one filter, the above dependency is going to determine the 'cut-off' frequency of the second filter.

So would you explain how you're configuring a transition width (or crossover width) independently of the number of coefficients?

Originally Posted by CopperTop

Just a question about the ideas behind active crossovers.

From what I understand, a steep crossover is desirable for reasons of relieving the drivers from being driven by 'unsuitable' frequencies, and also to eliminate multipath phase cancellation/addition from two drivers being driven simultaneously and the listener being off-axis.

In my setup I am driving a pair of sacrificial Mission 702e two way speakers with a home-brew PC-based crossover configured as follows:

FFT-based linear phase filtering
FFT size: 32768
Crossover frequency: 2-9kHz selectable.
Crossover width: 50-1000 Hz selectable.
Crossover filter characteristic: linear attenuation from unity to zero over the selected crossover width

I haven't done any 'voicing' of the setup as such, merely setting the amps to give equal levels from woofer and tweeter at 3kHz, and noting that for these particular drive units they seem more-or-less in phase over the crossover region at sensible frequencies. It sounds strikingly good 'out of the box' - in some ways the best hi fi I've ever heard. I have a calibration mic ready (no anechoic chamber unfortunately!), but I am not expecting to be able to make any great improvements, and probably it'll make it worse...

I can change the crossover frequency and width in real time (rough and ready GUI screenshot enclosed).

What I find is that I can hear the effect of the cutoff frequency fairly readily, certainly at the extremes, but I have to say that I cannot hear any effect whatsoever from the crossover width. Zero. I know that, in theory, the steep crossover gives more pre- (and post-) ringing but I have yet to hear it at all. Similarly, I know that the shallower crossover should cause multi-path effects if I move up and down in relation to the speakers while listening, but again I can hear no difference whatsoever!

How audibly significant have other active crossover users found the steepness to be?

[CopperTop]

Hi chaparK

Originally Posted by chaparK

My understanding of what you're doing is that you're performing a convolution of the input with successively one low-pass and one high pass. You obtained the impulse response of these filters (the 2 syncs) by computing the inverse Fourier transform of a brick-wall filter.

Not quite. The idea is to fade out the bass and fade in the treble over a specified band. The nearest I get to a brick wall is opting to do this over a narrow 50Hz width, but I can choose a width of up to 1000 Hz. In the image attached to the first post, below the 'buttons' there is a graph showing the two filters' frequency responses and the way they linearly fade in and out with frequency. In that particular example, the crossover width is 500 Hz.

Now when you associate a low-pass and a high-pass in a system, you have probably defined a dependency between these filters. One typical dependency is to require constant (or flat) output of the summed response Low-pass + High-pass.

Yes, for these my first forays into active crossovers (well, any crossovers at all!), I am simply aiming for a constant sum from the two filters. However, I would like to have the option of performing separate corrections on each driver.

So would you explain how you're configuring a transition width (or crossover width) independently of the number of coefficients?

By steering clear of very steep crossovers, I am assuming that a large FFT (I can live with the latency) will give me 'sufficient' coefficients to allow me to produce a pretty accurate crossover with any desired width. In the image attached to the first post, the frequency responses shown are plotted from the forward FFTs of the impulse responses after windowing, showing that the shape of the linear transition is virtually unchanged. I'll admit a linear transition is pretty ugly, and intuitively a smoother shape would seem nicer (and I did implement a sinusoidal-shaped roll-off at first) but is there any innate reason why a linear transition cannot be used?

[Mark.Clappers]

Take a look at this thesis paper: http://www.acoustics.hut.fi/~mak/PUB...57_6_PG413.pdf

Very interesting piece!

[sreten]

Originally Posted by CopperTop

And the advantage of low order slopes is..?

Hi,

For analogue filters the amount of phase wrap implied by the acoustic slope.

e.g. if you can get it to work properly (not easy) 2nd order L/R acoustic
sounds better than 4th order L/R acoustic, and note these functions are
not the electrical functions applied to the drivers.

rgds, sreten.

Take a look at the x/o's here : Zaphaudio.com

[Mark.Clappers]

Hi Sreten,

I agree completely with your analysis, however, I think the phase wrap is not very audible if it matches up between the overlapping drivers. The ringing effect of all filters but especially high order filters is more important to perceived sound quality.

So go as low as possible with your filter slopes but within the restrictions the drivers / cabinet make on your design.

Just my 2c!