To exeraggerate the nonlinearity of a loudspeaker, we cut the cone of
a mishandled driver as shown in Figure 10. We monitored the sound
pressure several centimeters in front of the dustcap using an Audio
Technica AT4049a microphone, which has a flat magnitude response to
within 3dB from 100Hz to 5kHz. The output from channel 1 of the
PreSonus sound interface was connected to the speaker via a power
amplifier, and the microphone was connected to the microphone input of
channel 1 on the sound interface. The following results are typical
of sine sweep measurements
to show how with a weakly nonlinear motor.

Inverse filtering the measured response results in
Figure 11, which is a plot of
nonlinear2ImpResp.wav.
The linear contribution corresponds to the spike at the beginning,
while the weakly nonlinear terms are clustered closer to the end of
the response.

The main linear contribution is cut out and plotted in
Figure 12. The measurement was not made in an
anechoic chamber, so there is a reflection about 15ms after the main
impact.

The nonlinear terms are shown magnified in
Figure 13. The lower order nonlinear terms
toward the right have larger magnitude but overlap less in time (see
Figure 13). Note that (Reference)
implies that the overlapping could be reduced by increasing the total
length TT of the sweep excitation signal.

The magnitude and phase responses corresponding to the linear impulse
response term from Figure 12 are shown in
Figure 14 and Figure 15 in *blue*. For
comparison, another sine sweep measurement was made at a lower level
so that the speaker behaved approximately linearly. Decreasing the
level also resulted in more noise and even some systematic error, as
is evidenced by the *red* curves in Figure 14 and
Figure 15. This comparison demonstrates that making
measurements at larger levels can reduce the effects of noise, while
nonlinear motor effects can be overcome with the sine sweep
measurement technique.

Comments:"A clear explanation of estimating impulse responses in acoustic signals using Golay codes and swept sine waves."