"Paul Guy" wrote in message

On Sat, 7 Aug 2004 07:02:36 -0400, "Arny Krueger"
wrote:

....stuff deleted........

I think that the triple tone test and modern spectrum analyzer
technology provides valuable insights into this area. I think that
I've established that when there are two upper-frequency probe
tones, FM distortion will produce sidebands with a higher amplitude
with the highest frequency tone, all other things being equal. This
finding can be, and probably should be applied to investigations
relating to both Doppler distortion and jitter.

To get an idea of the magnitude of any Doppler (FM) artifacts, you
need to know the cone velocity. It is my understanding, that in the
area where a speaker has a flat response, the velocities are fairly
consistent as frequency changes. So within this area, you should be
able to analyze and predict the Doppler effects.

I don't have much data that represents typical cone velocities at
different power levels (or SPL level, at say, 1 meter). From some of
the data shown on the Linkwitz site, he has a woofer with about 1.5
Meters/sec at 86db @1meter (that's reasonably loud). Does anyone have
typical data for other loudspeakers, especially at higher frequencies
(tweeters, midrange)?

If you can't see the motion, it must be 1/16 or less. Multiply the maximum
motion by 2 pi F to get peak velocity. Remember that peak possible cone
motion happens just below system resonance, and is less at higher
frequencies.

Using 1.5 M/s peak cone velocity, the speed of sound is about 340
M/sec, that should vary all the frequencies whose velocities were
supposed to be something else. Usually for the purpose of analysis, we
assume that all the other ones are pretty small. Anyhow, with those
numbers, you get about 0.44% change in frequency, higher or lower
depending which way the cone is moving.

Seems about right.

If the signal causing the 1.5
meter/sec was 50 Hz , and you had another signal of 4 KHz, then your
4khz note appears to be changing from 4khz to 4017 khz, then back then
to a low of 3983 khz, 50 times a second. In the frequency domain (your
ears, spectrum analyzer) things get weird.

Well, they get Besselized. ;-)

The result frequencies
(there are more than what you put in) depend on the ratio of the
change in frequency divided by the modulating frequency - this is the
modulation index - M. The total energy is unchanged, so that the
addition of extra stuff comes at the expense the main peak (unlike IM
distortion, where the modulating frequency has to add energy). If the
modulation index is less than 0.3, then there are 2 extra frequencies
(distortion), each one has an amplitude of 1/2 times M (modulation
index), or the total grunge is M . For low values of M, you get 2
extra freq., the sum and difference (just like IM distortion, but out
of phase with each other, and may sound QUITE different) . At higher M
the calculation is very complex, you can have almost all distortion
with almost no fundamental.

Agreed.

Using the above numbers, change in frequency is about 17 Hz,
modulation freq. is 50 Hz, so M=0.34 , or about 17% for each extra
frequency. These will be at 4050 and 3950. This is NOT IM distortion.

Well, its not AM distortion. Whether FM distortion is IM is controversial. I
think that FM is IM because that's what the words seem to mean to me.

The thing to note is that theamount of distortion changes with
modulating frequency! At 10Hz modulating freq,. M is about 1.7 - that
will mess up the waveform badly. The worst case is when the
frequencies are very different. With high values of M, the note
spreads out in frequency - instead of a fundamental and two satellite
tones, there is an almost contiuous block of frequencies. With a 5 or
10 Hz modulation, instead of 4 KHz and 2 extra peaks, you get an
almost continuous band of frequencies around 4 KHz.

That agrees with experimental results. However, you can get a similar family
of tones if your modulating signal is not a pure sine wave.

The sound? High M values are VERY noticeable, usually a warbling
sound, or noticeable extra frequencies. As M decreases to about 0.3,
the original pure tone sounds indistinct in pitch, or you might just
notice extra "stuff", and as M decreases to less than 0.1, it's very
hard to tell (for me). These were done at 4 KHz, with varying
amplitudes and frequency of the modulation frequency. This was not a
really good listening test, the real Golden Ears might be better at
finding the threshold. I used 2 signal generators, one modulating the
others frequency.

One can also use the tone generator in Audition/CE or a bunch of other
software. Then, everything is rigidly phase locked.

I used a spectrum analyzer to determine M, and
adjusted the signal generators to vary M as I listened to the "tones".
My good signal generators are at work, so if you're interested, I can
compare IM and FM (Doppler) distortion with the same frequencies.


I'm
sure Arny has the equipment more readily available - and may even have
.wav files for your listening pleasure, so you can hear for yourself
what the effects are.

Slightly different context, but its all FM:

http://www.pcabx.com/technical/jitter_power/index.htm

What would be really nice, is to frequency shift
a chunk of music with different delta-freq, and different modulation
frequencies, i.e., varying M with different conditions. Multi-tone and
real music should the preferred way to check this out.

It's just a matte of twidding in the parameters with software like
Audition/CE.

The cure? Keep wide ranges of frequencies OUT of a loudspeaker,
i.e., use 2 or 3 way systems. Because the modulation index (M) is
calculated with the modulating frequency as DENOMINATOR, avoiding low
modulating frequencies reduces the distortion. That bears out in my
listening tests. As the modulating frequency increases, the less
noticeable things are. A 3 way system can have a 10 to 1 range of
frequencies for each driver, compared to almost a 1000 to 1 range for
a singe wide range speaker. That will make a big difference when you
calculate M, the modulation index.

Agreed, and since 2-way speakers are almost endemic.., and get to be 3-way
when subwoofers are added...