To compute the amplitude
at the output of the
th subband,
we can apply an *envelope follower*. Classically, such as in the
original vocoder, this can be done by full-wave rectification and
subsequent low pass filtering, as shown in Fig.G.10. This
produces an approximation of the average power in each subband.

In *digital* signal processing, we can do much better than the
classical amplitude-envelope follower: We can measure instead
the *instantaneous amplitude* of the (assumed quasi sinusoidal)
signal in each filter band using so-called *analytic signal*
*processing* (introduced in §4.6). For this, we
generalize (G.3) to the real-part of the corresponding
analytic signal:

In general, when both amplitude and phase are needed, we must compute two real signals for each vocoder channel:

We call the

In order to determine these signals, we need to compute the analytic
signal
from its real part
. Ideally, the imaginary
part of the analytic signal is obtained from its real part using
the *Hilbert transform* (§4.6), as shown
in Fig.G.11.

Using the Hilbert-transform filter, we obtain the analytic signal in ``rectangular'' (Cartesian) form:

(G.7) |

To obtain the instantaneous amplitude and phase, we simply convert each complex value of to polar form

(G.8) |

as given by (G.6).

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