Commuted Synthesis
                           with
                      Acoustic Guitars

    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:

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The string and the resonator may be commuted, since the body and the string are nearly
linear and time invariant filters or LTI filters.

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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.

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    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