I was trying to say, that an analogue crossover is minimum phase, whereas a digital one could be anything...
I seem to recall hearing that the 1st order XO is minimum phase, but I am not sure about the higher order ones?
I was trying to say, that an analogue crossover is minimum phase, whereas a digital one could be anything...
No, if you want to see how a single frequency is affected you should look at the phase delay. If we take the filter from my earlier post (yesterday at 7:56 PM in my timezone) and feed it a single sine wave at 10kHz, we get the following response:Why is it meaningless? What if you want to know how the input signal is affected, even if it is a single frequency? The group delay curve will help inform, won't it?
Please provide an example that explains this, to help me.
I think it's misleading because you sort of imply that it's tricky to make a linear phase FIR filter. It's really not, you can choose any coefficients as long as they're symmetrical. Here's the frequency response of a filter with coefficients [0.5, 1, 0.5] running at 48kHz:I'm not sure how it's misleading? I just referred to a well-known class of FIR digital filters, not all classes of digital filters. It was but one example. Please provide some information on some design approaches other than that used by Parks–McClellan.
Yes, a pair of low-pass and high-pass first-order Butterworth filters sum to unity with zero phase shift at all frequencies. Hence, such a combination is minimum phase in nature, and is sometimes labelled as being "phase coherent".I seem to recall hearing that the 1st order XO is minimum phase, but I am not sure about the higher order ones?
However, mathematically the system impulse response is usually sharpened by adjusting the phase versus frequency.
Rather than argueing that the phase is not able to be heard, we could ask if the system‘s impulse response should be sharp?
Phase : angular position at time T on the wavefrontThankyou all for your earnest replies and discussion. So based on what I have read, might I get you guys to look over my current understanding?
Phase: The phase of a signal can be understood as a "shift" in the soundwave from its source, measured as an angle between 0 and 360 degrees.
Phase Delay: Different frequencies can (through filters or speaker design?) exhibit different delays. This would be called Phase Delay.
Minimum Phase: I'm not sure what this means yet and how it plays into group delay.
Group Delay: This would be the derivative of the Phase Delay graph. I suppose it tells us how 'chaotic' a device's frequency response is respective to its surrounding frequencies?
I wonder why Phase Delay and Group Delay are discussed somewhat separately. i.e. can we not infer group delay from phase delay? What is the benefit in focusing on one over the other?
I also wonder about the relationship between Group Delay and Distortion. For audibility, is lower group delay preferred?
Why is it also that there is much higher group delay in the bass region, and what tends to cause spikes in group delay (i.e. in many headphone measurements)?
Thank you Frgirar!By Neumann
What is “group delay” and how does it affect sound quality?
In simple terms, group delay is the time it takes for an electrical input signal to become an acoustical output. It is frequency dependant and should ideally be zero seconds at all frequencies, but this is practically impossible.
I find it hard to associate the word "sharp" with the looks of IR - is it really how you say it Down There?
Ok, let's get few things straight. Pretty much the only thing that introduces phase deviation in a passive speaker system is coming from the passive XO phase shift. Once you correct that phase shift with the FIR filter you will fix the looks of IR, but, as I already showed, the GD will remain pretty much the same.
You should be aware that, when EQ-ing the phase od the speaker, the target is not to flatten GD to zero but to flatten the excess phase graph to zero. Now, you could flatten the GD to zero as well, but that would introduce so much pre-ringing and that would, by all means be audible in a nasty way, while that typical rise in GD at low frequencies usually is not problematic at all.
What about the natural response of the tweeter/midrange/woofer drive units? Being minimum-phase electrodynamic transducers, they also have some phase shifts of their own. Each of those drivers is a bandpass system, with its own low-pass and high-pass cut-off frequencies and associated roll-offs. The natural magnitude and phase response of each such driver needs to be accounted for when the crossover filtering is being designed.Pretty much the only thing that introduces phase deviation in a passive speaker system is coming from the passive XO phase shift.
That will depend on what one is trying to achieve. Ideally, the multi-driver system would end up having a bandpass magnitude response function, completely flat in the passband. It would also be beneficial if it had a linear phase response (constant group delay). The excess phase is a concept related to comparing the difference between a minimum-phase system and one that isn't.You should be aware that, when EQ-ing the phase of the speaker, the target is not to flatten GD to zero but to flatten the excess phase graph to zero.
It's not entirely proven that the pre-ringing on an FIR filter such as the one suggested here is audible, let alone in a nasty way. The filter impulse response will be convolved with the input signal, and the resultant signal passed through the analog loudspeaker system. A linear-phase FIR-corrected loudspeaker system will have the ability to reproduce a waveform that maintains all the relative phases of the various frequency components of the input signal. It will produce a more faithful rendition of the input signals, be they transient ones or more steady-state ones, or combinations thereof.You should be aware that, when EQ-ing the phase of the speaker, the target is not to flatten GD to zero but to flatten the excess phase graph to zero. Now, you could flatten the GD to zero as well, but that would introduce so much pre-ringing and that would, by all means be audible in a nasty way, while that typical rise in GD at low frequencies usually is not problematic at all.
In general, multi-way passive loudspeakers are not minimum-phase systems; they have an excess phase component as part of their phase response. It is possible to apply minimum-phase analog equalization to such loudspeakers, where the change in amplitude corresponds to a particular change in phase response.Minimal phase : a system where a change in amplitude corresponds to a change in phase
It's not entirely proven that the pre-ringing on an FIR filter such as the one suggested here is audible, let alone in a nasty way.
@thorvat If it's not too much trouble, could you please point me to one or two posts that, in your opinion, provide good examples of the audibility of the preringing effect? Cheers.It has been proved, many times - you just need to put effort to dig for it. You can even find examples of sound files with audible preringing on this forum, you just have to search for it.
@KTN46 Can you point to a headphone measurement that has a spike in the group delay that you refer to?Why is it also that there is much higher group delay in the bass region, and what tends to cause spikes in group delay (i.e. in many headphone measurements)?
IIRC it was posted by @UliBru (Dr. Uli Brueggemann).
It took me quite a long time to recognize pre-ringing myself -- only after using rather "extreme" levels of phase manipulation with rePhase.