ee461@rochester.UUCP (VLSI class) (08/04/83)
>From rabbit!jj: "Furthermore, when the gentleman's tweeter was out of phase,
the speaker with the improperly phased tweeter (...) had a large zero in its
frequency response due to the improperly phased speaker."
Huh ? Say what ?? Large zero ??? No way, the crossover will mess the phase so
that a total cancellation will not occur (if the initial design was good) OK,
here I come with some equations: Assume a 2-way speaker + 1st order crossover
+ some idealization (flat response and no phase shift introduced by drivers
itself). The transfer function for the woofer is: TW(f)=1/(1+jf/f0), for the
tweeter: TT(f)=(jf/f0)/(1+jf/f0), where f0 is the crossover frequency. Your ear
gets a sum of these signals, so when everything is correct, the total transfer
function is TW(f)+TT(f)= 1. IT IS FLAT, both phase and amplitude, which explains
why a 1st order crossover is nice to have in your speakers. Now switch the
polarity of the tweeter; you get TW(f)-TT(f)= (1-jf/f0)/(1+jf/f0). THE
AMPLITUDE RESPONSE is 1! No big zeros! Instead, there is a nice, smooth,
continuos phase shift totaling 180 degrees over some 2 decades. Now back to
CD players (the one with 180 degree phase shift): they utilize some quite steep
ultrasonic filters; 4-th order seems to be a reasonable guess. Associated slope
of the phase response is 180deg/decade, therefore it would appear that the
particular CD player could have the sloping part of its phase response
contained roughly between 2 and 20 kHz. Nice, smooth and continuous shift.
THEREFORE: the effect encountered in the CD player with phase response screwed
up is roughly of the same nature as the effect obtained by switching the
polarity of the tweeter in a speaker with the 1st order crossover. The
difference is in the span of frequencies where the change occurs.
QED
So there. Now a rough estimate of how much nouniformity can be expected
from a regular speaker, with a 4th order crossover. Idealization as before.
Assume transfer functions with 4th degree poles, e.g.: TW(f)=1/(1+jf/f0)**4,
TT(f)=(jf/f1)**4/(1+jf/f1)**4. Note, that f0 is NOT equal to f1, as otherwise
there would be a nice -9 dB dip in the amplitude response at f0=f1. Rather, f0
and f1 are chosen in such a way, that -3dB points of each transfer function
coincide, which means that roughly 0.64*f0 = 1.71*f1. I.e., there is
about 1.5 octave difference between f0 and f1. The resulting misalignment
between phase characteristics causes a 90 deg peak, followed by a 90 deg dip
in the resulting phase response (all numbers approximate). These changes occur
on a span of some 7 octaves, with the distance between the +90 and -90 points
some 4 octaves, i.e. slightly more than a decade. This would be an answer to
the question about relative comparison between phase responses of speakers and
CD's that originated this discussion.
As for the perceptible effects of the phase shift, I start to suspect that
this is a largely subjective issue. For example, Keith Ericson wrote that
after experimenting with the polarity of his speakers he could not
definitely decide which sounded better. I think that phase coherent speakers
sound much more realistically. He apparently quotes somebody's opinion
that human ear is more sensitive to time delay than to the phase shift.
I've read opinions (in Abso!ute Sound) that were quite opposite and guys
argued there that it is phase that makes all the difference. It appears that
everybody should pick his own conclusions accordingly to his preferences. I'm
just wondering how much the general preferences (and reviewers of HiFi
equipment) were affected by getting accustomed to the sound of the abundance
of mediocre speakers all around.
Krzysztof Kozminski
(ee461@rochester)michaelk@tekmdp.UUCP (Michael Kersenbrock) (08/05/83)
Actually it is time delay that is the "culprit". The "technical" name for
distortion in this domain is "group delay distortion". You remember my comments
about moving your head 0.3 inches? Those comments are testable, reproduceable
effects. Put your speakers out in a open field (to eliminate effects that
we are not testing (like reflections)) and put into it a
1Khz tone or 20Khz tone . Put a microphone some distance
from it, with a scope attached (trigger off another -- but stationary --
microphone). The phase changes such that 360 deg.
phase shift happpens in about 1100/f feet. The wavelength of 20Khz is
about 0.6 inches, and about a foot for 1Khz. When you move your head/microphone
forward and back 0.6 inches, the 20K changes 360 degrees, the 1Khz
changes 18 degrees -- it is obvious because the wavelengths are different.
If it can be easily demonstrated for a SIMPLE test case, it is definitely
true for a complex case although *identification* of the cause/effects would be
more difficult. Now then, what is my real point? It is this: when you
move your head (we are in a field remember, no reflection effects) there
is no perceivable difference, certainly not with 0.3 inches (180 deg. at
20 KHz). THIS IS BECAUSE THERE IS A CONSTANT TIME DELAY. The different
frequencies PROPAGATE AT THE SAME SPEED (group velocity).
The distortion that we are really looking at is called group delay
distortion -- which means the frequency domain components for a particular
sound-mechanical or waveform-electrical signal don't arrive at the
same TIME in order to produce the same time domain signal that was started
with. Group delay distortion IS related to phase,but is NOT just phase response.
Group delay itself is the *first* derivative of the phase response, and
group delay distortion (the part you want to be zero) is the *second* derivative
of the phase response. It doesnt matter how much delay you have, just as long
as all frequencies have the same delay (like how far you are from the speakers).
I seem to recall that at least some if not most of the CD players
use a seventh order filter. The reason for such a high order is twofold.
First, they want a sharp cutoff above 20 Khz. Secondly, they want zero
group delay distortion. Filters with zero group delay distortion have
a very slow amplitude rolloff, and so it takes a high order filter to
accomplish both goals. There is a great opportunity here for digital-domain
filtering .
Mike Kersenbrock
Tektronix Microcomputer Development Products
Aloha, Oregonnewman@utcsrgv.UUCP (Ken Newman) (08/06/83)
Regarding comment on digital filtering, the Magnavox FD-2000SL cd player uses this technique. Quotes from July 83 High Fidelity: "Unlike most of the Japanese units, the Magnavox/Philips players do not use 16-bit digital-to-analog converters, which the company believes are not yet good enough for this application. Instead, they use 14-bit chips, with 4:1 (176.4 kHz) oversampling and digital filtering to achieve a 16-bit equivalent S/N ratio. This also permits the use of an output-smoothing filter with a relatively shallow slope of 18 dB per octave, for better phase response in the audio band..." "Both the square-wave and impulse responses are very good, undoubtedly because of Magnavox's novel filtering scheme. Note the perfect symmetry..." (This player also has superb tracking of defects on test disks, is the smallest cd player around, and is also the cheapest at $800 US).