96
D. Rocchesso: Sound Processing
subtractive synthesis
excitation signal
allpole filter
pitch shifting
time stretching
data reduction
digital oscillator
5.1.3
LPC Modelling
As explained in section 4.2, the Linear Predictive Coding can be used to model
piecewise stationary spectra. The LPC synthesis proceeds according to the feed-
forward scheme of figure 5. Essentially, it is a subtractive synthesis algorithm
where a spectrally-rich excitation signal is filtered by an allpole filter. The exci-
tation signal can be the residual e that comes directly from the analysis, or it is
selected from a code book. Alternatively, we can make use of voiced/unvoiced
information to generate an excitation signal that can either be a random noise
or a pulse train. In the latter case, the pulse repetition period is derived from
pitch information, available as a parameter.
a , ..., a
1
P
Excitation
Synthesis
v/uv
pitch
e
RMS amplitude
Allpole
Filter
Figure 5: LPC Synthesis
Between the analysis and synthesis stages, several modifications are possible:
· pitch shifting, obtained by modification of the pitch parameter;
· time stretching, obtained by stretching the window where the signal is
assumed to be stationary;
· data reduction, by model order reduction or residual coding.
5.2
Time-domain models
While the description of sound is more meaningful if done in the spectral domain,
in many applications it is convenient to approach the sound synthesis directly
in the time domain.
5.2.1
The Digital Oscillator
We have seen in section 5.1.1 how a complex sound made of several sinusoidal
partials is conveniently synthesized by the FFT
-1
method. If the sinusoidal
components are not too many, it may be convenient to synthesize each partial
by means of a digital oscillator.
From the obvious identity
e
j
0
(n+1)
= e
j
0
e
j
0
n
,
(6)
said e
j
0
n
= x
R
(n)+jx
I
(n), it is evident that the oscillator can be implemented
by one complex multiplication, i.e., 4 real multiplications, at each time step:
x
R
(n + 1) = cos
0
x
R
(n) - sin
0
x
I
(n)
(7)
x
I
(n + 1) = sin
0
x
R
(n) + cos
0
x
I
(n) .
(8)