In a guitar the
signal from a string couples into a resonating body which then acts like
an amplifier.
Like in many string instruments
sound in a guitar is tranduced via the bridge into the body. This
body
inturn imposes its own frequency
response on the sound. Normally in a guitar an excitation
is caused
by the plucking of a string by a fingernail or pick.
This excitation sends a signal that travels directly to
the bridge. Once in the body the signal is coupled
with the surrounding air and we hear the result.
The schematics of a stringed musical instrument:
***
The string and the resonator may be commuted, since the
body and the string are nearly
linear and time invariant filters or LTI filters.
***
The excitation and the resonating body can then be convolved
to form an aggregate excitation.
This greatly reduces the complexity of the stringed instrument
implementation. by eliminating many
steps in the modeling.
***
In the implementation of a guitar the
aggregate excitation can be generated using a sharp tap on the
bridge. The Frequency response is recorded using
a microphone a few feet away from the guitar to make
sure that the resulting recording is not to long.
It is better to avoid direct signals from the sound hole because
it is easy to pick up the resonances of the air within
the guitar. The impulse response used on this example
is quite rough. There is a Backround hum and the
tap was not quite sharp enough. For best results
a force hammer should be used for the tap and an accelerometer
shoud be mounted on the bridge to obtain
a clearer more accurate signal.
Two functions were used to model the
guitar. First was a low pass echo filter used to model the attack
and decay of a stringed instrument ( Filter
Code ). The bodies frequency response was used
as the initial excitation
for the string model. The second was an FIR echo function
used to delay and reflect the wave form to create
the bipolar model (Echo Code
). This was done to simulate the point of attack on
the string.
Sample Sounds (wav files):
Modeled Guitar: A 440 Modeled
Guitar
Real Guitar: A 440 Classical
Guitar
Modeled Classical Guitar:
Real Classical Guitar Frequency Analysis:
*** Diagrams Were Obtained at: http://www-ccrma.stanford.edu/~jos/waveguide/Acoustic_Guitars.html