Biomedical Engineering Reference
In-Depth Information
2. Use the values of
x
to generate the sound pressure fluctuations and dis-
placements at the end of the tract.
3. Normalize these values and write them in binary format.
We are then ready to listen to our sounds. Windows operating systems are
distributed with a sound player among their accessories, and a variety of
sophisticated options are common. Linux is also distributed with sound play-
ers, and many distributions also come with
snd
, an open-source sound player,
recorder and editor.
It should be pointed out that we are working under the source-filter the-
ory, which states that a vibrating valve in the avian vocal organ is capable of
generating a multifrequency signal, which is then filtered (see Chap. 6). Are
there many bird sounds which are generated by mechanisms compatible with
this hypothesis? Pure-tone birdsong, for example, is a common phenomenon
in birds. Since these sounds are spectrally “pure”, and sound “whistled”,
many hypotheses have been proposed to account for them. For example, it
is possible to think of tube resonances coupling to a vibrating valve, sup-
pressing the normal production of harmonic overtones. In order to settle this
issue, Beckers and coworkers recorded sound signals close to the syringeal
sound source during spontaneous pure-tone vocalizations. At least for turtle-
doves, these authors could show that pure tones originate through filtering
of a multifrequency harmonic sound source [Beckers et al. 2003a].
7.2 Analog Integration
If we feel uncomfortable around computers, we can actually build an ana-
log integrator of the equations defining our model, and physically listen
to the synthetic songs by connecting it appropriately to a loudspeaker
[Reuter et al. 1999]. In this section we describe a very simple analog syn-
thesizer, built with commercial electronic components.
7.2.1 Operational Amplifiers: Adding and Integrating
Our main building block is the
differential amplifier
, a device with two inputs
(positive and negative, or noninverting and inverting) as shown in Fig. 7.1,
with an output voltage
V
out
=
A
(
V
+
−
V
−
), where
A
is the gain. A special
form of differential amplifier, the
operational amplifier
or
op-amp
, is widely
used. It has an extremely large gain (typically on the order of 10
6
). In fact,
in use, these devices are connected to power supplies of about
±
15 V, which
of course bounds their amplification gain.
As described above, it would seem that op-amps are useful only for tiny
signals, but these devices are used with connecting impedances between one
of the inputs and the output, which provides a negative-feedback loop. Under
these conditions, the op-amp will operate in such a way that the following
conditions apply:
