There is a school of thought that says the only way to accomplish a linear phase crossover is to use linear phase filters which are a special class of FIR filter that sums to a unity response with a fixed time delay. So when both high pass and low pass sections are added together the response is a delayed version of what is being fed into the crossover. As I have discussed in another thread this type of filter has issues with proper impulse response cancellation due to imperfect matching between drivers which can result in severe pre-ringing leakage among other topics. The proponents of these filters will never talk about this aspect of this type of filter topology, instead pretending that it doesn't exist or can easily be minimized so that it is never a problem.
The other way of linearizing the crossover is to take an existing non-minimum phase crossover and apply a global group-delay correction filter which is just an FIR filter with a large number of taps. The advantage here is there are no FIR filters in the actual crossover to generate any pre-ringing artifacts. This is the approach taken by a few commercial designs as well as here, although the correction filter usually requires a large number of taps and has a large delay depending on the sampling rate and tap count. So this should be taken into account if you want to use these speakers with other speakers or in conjunction with a video display in say a home theater system in order to avoid lip-syncing issues.
We took a four-way 8th-order Linkwitz-Riley crossover from one of our clients who own one of our Preamps and applied a global group-delay correction filter to linearize the phase response. The LR crossover was already flat but the phase response was anything but linear so a square wave fed into it did not look like a square wave coming out of it. A linear phase response means that there is just a time delay in the signal path whilst still maintaining a flat magnitude response but there is no waveform distortion.
To measure the phase distortion of the crossover in isolation we needed to sum the outputs of the crossover before they were level adjusted and time delayed so we could focus on the crossover alone without the effects of the speaker and the room etc which we know adds its own artifacts to the response. Later on, we will look at compensating for those as well but for now we are just focussing on fixing up the crossover and making sure the group-delay correction filter is doing its job properly.
To evaluate the crossover we just looked at one channel and summed the outputs to measure the net frequency response. We also fed the input to the crossover to one of the outputs of the preamp as a reference for the analyzer to create the frequency response. The summed outputs of the crossover are fed to another channel on the preamp. We also added a few multiplexers or selector switches to enable us to switch in and out various filters quickly so we can quickly evaluate the effects of different filter configurations. Both the input to the crossover and the summed outputs are then connected to our dScope III audio analyzer. The dScope III can measure both amplitude and interchannel phase. The following Audioweaver test bench is what we used to evaluate the effectiveness of the global correction filters.
All of the DSP is done on a PC instead of the Preamp itself because the group-delay correction filters required are beyond the resources of the onboard SHARC DSP. The Ultimate Preamplifier Plus (UPP) has a unique feature in that it allows one to run DSP on an external device such as a PC as though it was running inside the Preamp. In fact, in another thread, we proved that the audio path was transparent and the performance of the Preamp was unaffected by the noisy environment of a PC ! The Ultimate Preamplifier Plus can also share DSP between its own onboard DSP as well as an external PC so for example you could build a non-minimum phase LR crossover using the onboard SHARC DSP whilst running the correction filter on an external PC and then switch the correction filter in or out from the Preamp menu. This is the approach our client is taking but for proof of concept and convenience, we ran everything on an external PC which allowed us to quickly evaluate and test everything in the one environment. The main aim was to validate the effectiveness of the global group-delay correction filters and prove that you don't need to use dedicated linear-phase filters to achieve this.
First, we measured the frequency and phase response of the crossover filter alone using a log frequency axis. We note the flatness of the filter as expected but the phase is anything but flat ! The top blue trace is the sweep of the input which is ruler flat as expected and the bottom red trace is the crossover summation of all drivers which is also ruler flat as expected.
To evaluate the phase response we reran the frequency response test using a linear frequency axis instead of the usual log axis. If the phase is linear then the phase response should look straight and not curved. Since the analyzer cannot distinguish phase greater or less than 180 and -180 degrees respectively it wraps or folds the phase so the response always is contained within a 360 degree envelope which makes it look like a saw-tooth. From the phase plot below we can see the phase is anything but linear which was expected !
And now for the money shot. What does this crossover filter do to a square wave? The square wave is important because it is not just a single tone but rather a series of odd harmonically related tones with a monotonically decreasing magnitude. If the phase is not linear, it will manifest itself as distortion in the waveform even though the magnitudes of the harmonics are still correct. So, let's look at the test results on a scope.
Firstly at 1kHz and then at 100 Hz !! This is what a non-minimum phase crossover does to a square wave !! Can we fix this ??
The other way of linearizing the crossover is to take an existing non-minimum phase crossover and apply a global group-delay correction filter which is just an FIR filter with a large number of taps. The advantage here is there are no FIR filters in the actual crossover to generate any pre-ringing artifacts. This is the approach taken by a few commercial designs as well as here, although the correction filter usually requires a large number of taps and has a large delay depending on the sampling rate and tap count. So this should be taken into account if you want to use these speakers with other speakers or in conjunction with a video display in say a home theater system in order to avoid lip-syncing issues.
We took a four-way 8th-order Linkwitz-Riley crossover from one of our clients who own one of our Preamps and applied a global group-delay correction filter to linearize the phase response. The LR crossover was already flat but the phase response was anything but linear so a square wave fed into it did not look like a square wave coming out of it. A linear phase response means that there is just a time delay in the signal path whilst still maintaining a flat magnitude response but there is no waveform distortion.
To measure the phase distortion of the crossover in isolation we needed to sum the outputs of the crossover before they were level adjusted and time delayed so we could focus on the crossover alone without the effects of the speaker and the room etc which we know adds its own artifacts to the response. Later on, we will look at compensating for those as well but for now we are just focussing on fixing up the crossover and making sure the group-delay correction filter is doing its job properly.
To evaluate the crossover we just looked at one channel and summed the outputs to measure the net frequency response. We also fed the input to the crossover to one of the outputs of the preamp as a reference for the analyzer to create the frequency response. The summed outputs of the crossover are fed to another channel on the preamp. We also added a few multiplexers or selector switches to enable us to switch in and out various filters quickly so we can quickly evaluate the effects of different filter configurations. Both the input to the crossover and the summed outputs are then connected to our dScope III audio analyzer. The dScope III can measure both amplitude and interchannel phase. The following Audioweaver test bench is what we used to evaluate the effectiveness of the global correction filters.
All of the DSP is done on a PC instead of the Preamp itself because the group-delay correction filters required are beyond the resources of the onboard SHARC DSP. The Ultimate Preamplifier Plus (UPP) has a unique feature in that it allows one to run DSP on an external device such as a PC as though it was running inside the Preamp. In fact, in another thread, we proved that the audio path was transparent and the performance of the Preamp was unaffected by the noisy environment of a PC ! The Ultimate Preamplifier Plus can also share DSP between its own onboard DSP as well as an external PC so for example you could build a non-minimum phase LR crossover using the onboard SHARC DSP whilst running the correction filter on an external PC and then switch the correction filter in or out from the Preamp menu. This is the approach our client is taking but for proof of concept and convenience, we ran everything on an external PC which allowed us to quickly evaluate and test everything in the one environment. The main aim was to validate the effectiveness of the global group-delay correction filters and prove that you don't need to use dedicated linear-phase filters to achieve this.
First, we measured the frequency and phase response of the crossover filter alone using a log frequency axis. We note the flatness of the filter as expected but the phase is anything but flat ! The top blue trace is the sweep of the input which is ruler flat as expected and the bottom red trace is the crossover summation of all drivers which is also ruler flat as expected.
To evaluate the phase response we reran the frequency response test using a linear frequency axis instead of the usual log axis. If the phase is linear then the phase response should look straight and not curved. Since the analyzer cannot distinguish phase greater or less than 180 and -180 degrees respectively it wraps or folds the phase so the response always is contained within a 360 degree envelope which makes it look like a saw-tooth. From the phase plot below we can see the phase is anything but linear which was expected !
And now for the money shot. What does this crossover filter do to a square wave? The square wave is important because it is not just a single tone but rather a series of odd harmonically related tones with a monotonically decreasing magnitude. If the phase is not linear, it will manifest itself as distortion in the waveform even though the magnitudes of the harmonics are still correct. So, let's look at the test results on a scope.
Firstly at 1kHz and then at 100 Hz !! This is what a non-minimum phase crossover does to a square wave !! Can we fix this ??
