Exercises in Wave Digital Modeling
- Comparing digital and analog frequency formulas.
This first exercise verifies that the elementary ``tank circuit''
always resonates at exactly the frequency it should, according to the
bilinear transform frequency mapping
, where denotes ``analog frequency'' and
denotes ``digital frequency''.
- Find the poles of Fig.F.35 in terms of .
- Show that the resonance frequency is given by
- Recall that the mass-spring oscillator resonates at
. Relate these two resonance frequency formulas
via the analog-digital frequency map
.
- Show that the trig identity you discovered in this way is true.
I.e., show that
- Find the poles of Fig.F.35 in terms of .
Previous Section:
Energy-Preserving Parameter Changes (Mass-Spring Oscillator)