Digital Signal Processing Reference
In-Depth Information
this signal with a 3800 Hz modulation function a signal, as depicted in part (
b
)of
Figure 7.10, is generated.
Depending on the modulation frequency sometimes the spectrum resulting from
the negative shift and that of the positive overlap. For that reason bandpass filtering
might be necessary before applying the modulation function. Additionally the
output signal might contain signal components within the telephone band. This is
the case in the example that we have depicted in Figure 7.10. In those cases a filter
also can be applied—this time the filter is applied to the output
ˆ
bb
(
n
)—that lets
only those frequencies that are desired pass. Additionally the original signal, respect-
ively its whitened version
e
nb
(
n
), can be used within the telephone band.
The reason for performing such a shift in frequency can easily be understood when
we consider the processing of voiced utterances. The periodic signal that is typical for
voiced utterances can be extended by modulation techniques. By incorporating a pitch
detection one could even perform an adaptive shift and thereby keep the pitch structure
even at the transition regions from the telephone band to the extension area. As seen in
Section 7.4 the excitation signal of unvoiced utterances is noise-like and therefore we
do not have a structure we have to take care of. This means that we also can apply this
excitation extension method for unvoiced utterances without having to worry about
continuing the signal structure along the frequency axis.
Nonlinear Processing
One major problem of the above discussed modulation
techniques is the pitch detection if the algorithm is designed (pitch-) adaptive.
Especially in the low frequency part bothersome artifacts occur if, concerning
voiced utterances, the harmonics of the pitch frequency are misplaced. This means
that the performance of the algorithm crucially depends on the performance of the
pitch detection.
Another possibility to extend the excitation signal is the application of nonlinear
characteristics. Nonlinearities have the property that they produce harmonics when
applied to a periodic signal. This once again takes the case of voiced utterances
into account. There exists a variety of nonlinear characteristics which all have
different properties. A quadratic characteristic on one hand produces only even
harmonics. A cubic characteristic on the other hand produces only odd harmonics.
The effect of the application of a nonlinear characteristic can be explained best
for the quadratic characteristic. The application of a quadratic characteristic
in the time domain corresponds to the convolution of the signal with itself in
the frequency domain
e
bb
(
n
)
¼ e
nb
(
n
)
W
† E
nb
(
e
jV
)
E
nb
(
e
jV
)
¼E
bb
(
e
jV
)
:
(7
:
39)
If we assume a line spectrum in the case of voiced sounds the effect becomes clear.
Every time the lines match during the shift within the convolution, the resulting
signal will have a strong component. In contrast to the above presented method
where we had the convolution with a dirac at the arbitrary (or determined by a
pitch estimation algorithm) frequency
V
0
we convolve the signal with dirac impulses
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