You asked "why can't we". The answer is "we can".
You should probably be asking the question "why shouldn't' we" be doing that, or when should we do it and how should we do it.
I can think of a couple of disadvantages:
When you make the filters very steep, you get a rather abrupt change in directivity. Besides, you get a very poor phase response with minimum-phase filters and a very long pre-echo with linear-phase filters. The woofer's and tweeter's pre-echoes are supposed to cancel each other, but will never perfectly do so.
When you make the filters very steep, you get a rather abrupt change in directivity. Besides, you get a very poor phase response with minimum-phase filters and a very long pre-echo with linear-phase filters. The woofer's and tweeter's pre-echoes are supposed to cancel each other, but will never perfectly do so.
My experience with digital filters, is that you are making a compromise. You can never do something perfect. And when a midrange has to work in unity with a tweeter, because the theoretical best sound, comes from a single source - you then have to make both drivers blend seamlessly in a way, that you dont notice the crossover.
You could do the opposite of the first order filters and try to make a very sharp filter. But you have to remember that a driver is a mechanical device, which take time to move and stop again - and the size plays a role too. Furthermore - you have to be extremely precise, to make sure that the tweeter does absolutely what the midrange does not - and vice versa. Herein lies the rub. We easily hear when something is out of tune. So even though it might work in theory - my guess is, that it will sound less good, than with a bit of blending in the cross over region.
How much blending? - you might ask. Well.... some make something work - others dont.
You could do the opposite of the first order filters and try to make a very sharp filter. But you have to remember that a driver is a mechanical device, which take time to move and stop again - and the size plays a role too. Furthermore - you have to be extremely precise, to make sure that the tweeter does absolutely what the midrange does not - and vice versa. Herein lies the rub. We easily hear when something is out of tune. So even though it might work in theory - my guess is, that it will sound less good, than with a bit of blending in the cross over region.
How much blending? - you might ask. Well.... some make something work - others dont.
Would that be an issue in practice at the frequency a tweeter would take over?
What prompted this question is that in a number DSPs I have seen now they all offer the standard analogue filter curves. I understand this when EQing and when starting and ending the filter curves but for crossovers I would have thought we could have steeper curves almost to the point of on/off
I think that what you are envisioning in your mind is not possible. You just cant cut. But you can make very steep filters, like 5,0 khz = 0 dB and say, 6 khz = - 100 dB... that pretty "cut" but not completely cut which is what I guess you are thinking about.
Filters are math, and math says no to "cut".
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Filters are math, and math says no to "cut".
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I interpreted the question like this, admittedly a rather free interpretation:
With DSP techniques you can easily make a halfband filter bank where the sum of the output signals matches the input perfectly except for a constant delay, each output signal has the same perfectly constant delay, the low-pass output is within +/- 0.0000087 dB up to 2.9 kHz, at -6.020599... dB at 3 kHz and below -120 dB from 3.1 kHz onwards, and the high-pass output is below -120 dB up to 2.9 kHz, at -6.020599... dB at 3 kHz and within +/- 0.0000087 dB from 3.1 kHz onwards.
Why on Earth would anyone want to use a DSP to mimic an old-fashioned Linkwitz-Riley filter then?
With DSP techniques you can easily make a halfband filter bank where the sum of the output signals matches the input perfectly except for a constant delay, each output signal has the same perfectly constant delay, the low-pass output is within +/- 0.0000087 dB up to 2.9 kHz, at -6.020599... dB at 3 kHz and below -120 dB from 3.1 kHz onwards, and the high-pass output is below -120 dB up to 2.9 kHz, at -6.020599... dB at 3 kHz and within +/- 0.0000087 dB from 3.1 kHz onwards.
Why on Earth would anyone want to use a DSP to mimic an old-fashioned Linkwitz-Riley filter then?
Because humans can get their heads around them easily and they are cheap to implement in biquads.
Personally I like the idea of being able to swap between LR2 and LR4 or Transient perfect with just a few keyboard taps rather than soldering up different analog crossovers. But that's just me.
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