The analysis portion of PARSHL returns a set of amplitudes
, frequencies
, and phases
,
for each frame index
, with a ``triad'' (
) for each track
. From this analysis data the
program has the option of generating a synthetic sound.
The synthesis is done one frame at a time. The frame at hop
,
specifies the synthesis buffer
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(H.9) |
The parameter interpolation across time used in PARSHL is the same
as that used by McAulay and Quatieri [174]. Let
(
) and
(
) denote the sets of
parameters at frames
and
for the
th frequency track.
They are taken to represent the state of the signal at time 0
(the
left endpoint) of the frame.
The instantaneous amplitude
is easily obtained by linear
interpolation,
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(H.10) |
Frequency and phase values are tied together (frequency is the phase
derivative), and they both control the instantaneous phase
. Given that four variables are affecting the
instantaneous phase:
, and
, we need at least
three degrees of freedom for its control, while linear interpolation
only gives one. Therefore, we need at least a cubic polynomial as
interpolation function, of the form
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(H.11) |
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(H.12) |
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(H.13) |
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(H.14) |
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(H.15) |
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(H.16) |
Figure H.5 shows the result of the analysis/synthesis process using phase information and applied to a piano tone.
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