AN2834 Freescale Semiconductor / Motorola, AN2834 Datasheet - Page 3

• Manufacturer Part Number: AN2834
• Description: AN2834, Packet Telephony Automatic Level Control on the StarCore SC140 Core
• Manufacturer: Freescale Semiconductor / Motorola

where
typically required to avoid a level clipping effect on the signal. However, a very small step-size leads to undesirable
adaptation speed, so there is a trade-off in choosing the step-size for gain adaptation. The optimal step-size depends
on the predefined target signal level range of ALC devices. If P
(n –1)
The resulting gain adaptation sequence is:
Depending on the bandwidth of the low-pass filter used to estimate signal levels, the ALC gain adaptation
algorithm in Equation 3 may generate a gain bias. However, this bias is negligible when narrowband filters are
used, which is the preferred approach here.
If x(n) is a wide-sense stationary (WSS) signal, the ALC adaptive algorithm, using the signal level estimation as
per Equation 1, is expected to converge to an optimal gain, as shown in Equation 4:
where E{ } denotes statistical expectation. If the gain adaptation is implemented using a narrowband low-pass
filter, that is, one that uses a control parameter a close to one, the resulting optimal gain can be approximated in
Equation 5.
On the other hand, if the gain adaptation is implemented using a wideband filter, that is, one that uses a control
parameter a very close to zero, the resulting optimal gain becomes the one shown in Equation 6.
Therefore, the expected bias of the output signal level for WSS signals is given in Equation 7.
Freescale Semiconductor
1.
2.
3.
4.
5.
> 0 is a step-size controlling the rate of change of the gain signal g(n). A small adaptation step-size is
g(n) < g(n–1). Furthermore, as the input signal level P
Estimate the input signal level P
Update the gain signal g(n).
Generate the output signal y(n) = g(n) x(n).
Estimate the output signal level P
Repeat steps 1–4 for new samples of x(n).
g
opt
Packet Telephony Automatic Level Control on the StarCore SC140 Core, Rev. 1
a
g
b
=
a
=
P
ref
g
---------------- -
opt
E P
------------------------ -
E P
g
a
x
2
x
=
n
n
g
opt
x
(n).
y
-----------------------------------------------------------------------------------------------------
2aE P
(n).
=
g
0
=
=
-----------------------------------------------------------------------------------------------------
2aE P
x
-----------------------
E x
P
n 1
ref
P
–
2
x
ref
1
E x
-----------------------
E x
n
n 1
+
ref
x
P
x
–
a
2
(n) decreases, the gain adaptation tends to stop.
ref
2
4
> P
n
E x
n
n
1
x
y
2
(n –1)
+
+
2
n
a
n
1 a
E x
–
+
2
g(n) > g(n–1), and if P
2
1 a
Basics of Automatic Level Control
E x
–
n
4
E x
n
4
n
Equation 4
Equation 5
Equation 6
Equation 7
ref
< P
y
3