Measuring Loudspeakers, Part Two Page 4
Does a loudspeaker's time coherence matter? A "perfect" speaker, of course, would have both a perfect impulse response and a perfect frequency response (at one point in space). Another way of looking at a loudspeaker's time-domain performance is to examine its acoustic phase response, the phase angle between the pressure and velocity components of the sound plotted against frequency.
Again, this is an aspect of loudspeaker behavior that has proved controversial. One school of thought holds that it is very important to perceived quality; another, which includes almost all loudspeaker engineers, finds it unimportant. Floyd Toole, now with Harman International but then with Canada's National Research Council, in his summary of research at the NRC into loudspeaker performance that is described in two classic 1986 papers [32, 33], concluded thusly: "The advocates of accurate waveform reproduction, implying both accurate amplitude and phase responses, are in a particularly awkward situation. In spite of the considerable engineering appeal of this concept, practical tests have yielded little evidence of listener sensitivity to this factor...the limited results lend support for the popular view that the effects of phase are clearly subordinate to amplitude response."
This is also my view. Of the 350 or so loudspeakers I have measured, there is no correlation between whether or not they are time-coherent and whether or not they are recommended by a Stereophile reviewer. However, I feel that if other factors have been optimized—on-axis response, off-axis dispersion, absence of resonance-related problems, and good linearity—like a little bit of chicken soup, time coherence (hence minimal acoustic phase error) cannot hurt. In my admittedly anecdotal experience, a speaker that is time-coherent (on the listening axis) does have a small edge when it comes to presenting a stereo soundstage, in terms of image focus and image depth. But time coherence does not compensate for coloration, poor presentation of instrumental timbres, a perverse frequency balance, or high levels of nonlinear distortion.
In 1990, Rodney Greenfield and Malcolm Omar Hawksford  used DSP-based digital filters to try to separate the audible effects of a loudspeaker's phase error from its amplitude response error. The point was made that a semi-reverberant environment will tend to mask phase effects. In addition, when typical recordings are played, which may have undergone many phase-altering stages during production, the audibility of phase differences becomes moot: "one is simply detecting a change in phase distortion and not a correction of it and as such preferences would most likely be personal." Nevertheless, the authors "very tentatively" concluded that equalizing a loudspeaker's excess phase error modified listeners' perception of the apparent soundstage.
It is important to note that there are phase responses and phase responses. Not only is phase error associated with a lack of time coherence, phase error is introduced by any departure from a flat amplitude response. The phase response of what is called a "minimum-phase" system is related to the amplitude response by a mathematical function called the Hilbert Transform. So, for any nonflat system like a loudspeaker, it is important to distinguish between the two sources of phase error. The MLSSA system allows its operator to subtract the calculated minimum-phase, amplitude error-related phase response from the measured acoustic phase response. The result is what is called the "excess" phase response mentioned above. (Note that the MLSSA system does measure the actual acoustic phase. Some competing measurement systems calculate just the amplitude-related minimum phase response.)
Fig.16 shows a typical two-way loudspeaker's excess-phase response on its reference axis, plotted from the lower midrange upward in frequency. (Note that the time of flight of the sound from the loudspeaker to the measuring microphone has to be windowed out of the impulse response before the actual phase response is calculated.) It should be clear that this is not a time-coherent design. There's a negative or leading phase error that increases above 2kHz in a linear manner with logarithmic frequency.
Fig.16 Acoustic excess phase response of typical loudspeaker.
This negative-slope, approximately straight line in the frequency region covered by the tweeter means that there is a simple time delay between the tweeter's output and that of the woofer. The drive-units are mounted on a flat baffle, but a tweeter is physically less deep than a woofer, meaning that its acoustic center is closer to the microphone. Unless some time delay is introduced in the tweeter drive signal, a flat-baffle speaker will never have a flat excess-phase response.