Linear phase definition?

jhollander

So for a system to be called linear phase, how long/ far would the phase need to be continuous before wrapping?  From woofer LF roll off through 20K? Past  x-o by???

I agree that linear phase may not be distinguishable feature, I'm talking about "labeling" a system phase response.

dcibel

My understanding of the definition of linear phase, is the slope of the phase would remain constant over frequency. What the slope is would be dependant on the frequency response of the system.

Wolf

To my understanding, linear-phase does not wrap at all.

jhollander

The phase slope would never be constant in the mathematical sense unless the FR is completely linear/ first order.  I've always thought that all single driver systems were linear phase even those that don't cover much FR. 

So, for a 2-way as long as you don't wrap at the x-o would that meet the "linear" phase definition?

dcibel

jhollander said:

The phase slope would never be constant in the mathematical sense unless the FR is completely linear/ first order.  I've always thought that all single driver systems were linear phase even those that don't cover much FR. 

So, for a 2-way as long as you don't wrap at the x-o would that meet the "linear" phase definition?

Pretty much. Personally I don't think linear phase is the correct term, I think minimum phase is a more accurate description, or even "time-aligned". Basically, if the phase matches up with the minimum phase response of a filter that represents the frequency response of the system, than the system is minimum phase. This comparison is often made in the documentation of SoundEasy to determine or verify the start of the FFT to generate a minimum phase frequency response using a 2 channel measurement system.

Single drivers systems are "linear phase" for the simple fact that there is only one acoustic source. A system with more than one acoustic source has potential to be "phase aligned" at the crossover frequency, but this isn't necessarily time aligned, the second source could be off by a full 360 deg but still phase aligned, which raises the "time smear" concerns with a dynamic non-sine signal,  and introduces the "phase wrap" due to the excess phase of this time delay. In this case, the phase linearity can be analyzed by looking at the time domain of a square wave signal.

Here's a doc from the SoundEasy guy on the topic of linear phase:

http://www.linkwitzlab.com/Attributes_Of_Linear_Phase_Loudspeakers.pdf

jr@mac

Just a thought, 360 and 0 are the same point on a circle.

Wolf

This is true. Wrapping is just an artifact of displaying a 3D cylindrical curve in a 2D plot.

dcibel

A sine wave is just a circle over time (fun graphic). If all we needed was to playback sine waves, one acoustic source being off by multiple cycles would not be of a concern, the signal would still line up perfectly. But we are playing a dynamically changing audio signal, so when one acoustic source is off by a few cycles at a specific frequency, even though phase might be aligned, there is still a real time delay involved, the signal is not 100% accurate to the original source. IMO these small delays, especially at higher frequencies can have a significant effect on sound localization or "imaging".

Ed_Perkins

IIRC speakers (in general) are minimum phase devices, not linear phase.  

Wolf

That's correct, Ed. The Linear Phase has to do with the relationship of the drivers in the design.