In the following we consider the results for the saxophone model. The
model we present consists of 10 input units, 200 hidden units and 5
output units and was trained with additional Gaussian noise at the
input. The standard deviation of the noise is 
and the RMS
training error obtained is 
. The resulting saxophone model is
able to resynthesize a signal which is nearly indistinguishable from
the original one. The resynthesized time series is shown in
figure 2. The time series follows the original one with a
small phase shift, which stems from a small difference in the onset of
the model. Also in figure 2 the power spectrum of the
saxophone signal and the neural model is shown. From the spectrum we
see the close resemblance of the sound.
One major demand for the practical application of the proposed musical instrument models is the possibility to control the synthesized sound. At the present state there exists only one control input to the model. Nevertheless, it is interesting to investigate the effect of varying the control input of the model. We tried different control input sequences to synthesize saxophone tones. It turns out that the model remains stable such that we are able to control the envelope of the sound. An example of a tone with increased duration is shown in figure 3. In this example the control input first follows the trained version, then remains constant to produce a longer duration of the tone and then increases to reproduce the end of the tone from the trained time series.
Figure 2:
Synthesized saxophone signal and power spectrum estimation for
the original (solid) and synthesized (dashed) signal.
Figure 3:
Varying the synthesized tone by varying the control input sequence.