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Mass Momentum and Energy
Above we found the
mass
velocity
to be
when
is chosen for the
bilinear transform
The
momentum
of the mass is therefore
when
State variable
is
mass momentum per sample
Since momentum is conserved,
momentum
waves
are good to consider in place of velocity waves
The
kinetic energy
of the mass is given by
for
The
potential energy
of the mass-in-flight is of course zero (
)
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Download
WaveDigitalFilters.pdf
Download
WaveDigitalFilters_2up.pdf
Download
WaveDigitalFilters_4up.pdf
``
Wave Digital Filters
'', by
Julius O. Smith III
, (From Lecture Overheads,
Music 420
).
Copyright ©
2022-07-26
by
Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),
Stanford University
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