The results of the HiBall vs. Whisper comparison
were better with the conventional speaker than previous results obtained with
the flat speaker. However, the differences were still more than we had hoped.
This experiment was conducted to investigate the effects of speaker
orientation on the range measurements. The thinking was that the speaker
cone might be acting as many tiny "point emitters" and thus one
edge of the cone (for example) might appear to the Whisper system as a
physically separate emitter from the opposite edge of the cone. This might
result in a phenomenon similar to that observed for the flat speaker where,
as the speaker orientation changed wrt a particular microphone, parts of the
speaker that were acting as separate emitters would get closer while others
moved farther away. For the flat speaker, this resulted in four distinct
points in space competing to represent a single point. See the
flat vs. conventional speaker comparison
for more details.
This rotation experiment was performed informally during the
flat vs. conventional speaker comparison.
The results did not appear to exhibit the "multiple emitter problem."
However, the speaker was handheld during these trials, and thus a more rigorous
experiment needed to be performed.
To better control the rotation, an optical rotation stage was mounted
to an optical rail, with an xy stage mounted to the rotation stage, and
the speaker mounted to the xy stage. A microphone was then placed directly
in front of the speaker. Several 45-second trials were then performed to
fine tune the speaker location. Each trial began with the speaker directly
facing the microphone. Then the speaker was rotated 45 degrees clockwise,
then back to center, then 45 degrees counter clockwise, and finally back to
center again. The resulting range data was then plotted, and the xy stage
was adjusted. The intent was to get the center of the speaker aligned with
the axis of rotation.
A picture of the setup will be added soon. However, for now, letís just
move on to the results.
Figure 1 shows the resulting range measurement after the setup had
been calibrated to place the speaker directly over the center of rotation.
Figure 2 shows the same results with highlighted areas representing
stationary periods. The vertical axes represent chips (i.e. range).
Each chip is about three millimeters. The horizontal axes can roughly
be thought of as milliseconds. They are scaled by 104
and so a value of 1 (for example) corresponds to 10000 milliseconds or
Figure 1: Range results.
The experiment began with the speaker directly facing the
microphone. The motion of the speaker was as follows:
- The speaker was directly facing the microphone for approximately five seconds (Region 1 in Figure 2).
- It was then slowly rotated 45 degrees clockwise.
- It remained in this position for approximately five seconds (Region 2 in Figure 2).
- It was then slowly moved back to center.
- It remained in this position for approximately five seconds (Region 3 in Figure 2).
- It was then slowly rotated 45 degrees counterclockwise.
- It remained in this position for approximately five seconds (Region 4 in Figure 2).
- It was then slowly moved back to center.
- It remained in this position for approximately two seconds (Region 5 in Figure 2).
Figure 2: Range results.
Matlab standard deviation calculations appear below for two
portions of the range data. The first range, 1:5000, represents
data when the speaker was directly facing the microphone. The
second range, 10000:15000, represents data when the speaker
was turned away 45 degrees.
Since, in general, 96 percent of sample values fall with ±3
standard deviations, these results indicate that 96 percent of the
values are within ±0.070953 chips or roughly ±0.2 mm
when the speaker is directly facing the microphone. Similarly, 96 percent
of the values are within ±0.199248 chips or roughly ±0.6 mm
when the speaker is turned away from the microphone. Moreover, from the
plots above, all range values are within half a chip (that is, they are
all contained in the region from 68.5 to 69). Half a chip equates to
less than two millimeters.
The point is, we were interested in determining how much the range
changed as the speaker rotates, and the simple answer is "not very much."
Thus, it does not appear that speaker orientation is a significant factor.