AN2384 Freescale Semiconductor / Motorola, AN2384 Datasheet - Page 5

• Manufacturer Part Number: AN2384
• Description: Generic Tone Detection Using Teager-Kaiser Energy Operators on the StarCore SC140 Core
• Manufacturer: Freescale Semiconductor / Motorola

It can be shown that the following expression applies:
For the two-component case (N = 2), it is important to notice the following:
The values of the following are pre-computed and stored in a look-up table; if magnitude estimations are not
needed:
The gains may be ignored:
The following coefficients are pre-computed and stored in a look-up table.
To detect a given multi-component tone successfully, a self-tuning mechanism is required for searching the optimal
set of frequencies that minimizes variability of the frequency detector outputs. This self-tuning mechanism is based
on the fact that a single frequency tone generates a constant value after the TK energy operator processes it. The
self-tuning mechanism works as follows:
Figure 1 illustrates the structure of the multi-component detector, where a detected tone m
decision logic unit.
Freescale Semiconductor
1.
2.
3.
Generic Tone Detection Using Teager-Kaiser Energy Operators on the StarCore SC140 Core, Rev. 1
The process starts with an initial guess m = m
follows:
When the next sample is processed, magnitude and frequency estimates are computed, and the closest
pair of reference frequencies is selected, thus defining a new guess m = m
are then defined. In this process, the parameter r of the comb filters may also be adjusted.
This self-tuning process repeats until the optimal symbol (tone) m = m
the filter coefficients are fixed, resulting in frequency lock. If the signaling tone is removed, the fre-
quency is unlocked until a new tone is detected. The bandwidth of the LPFs can be adjusted (that is,
gear-shifted) by choosing different values of
(m)
c
=
i
c
( )
1 – r
2
2
b
– r [r cos (
c
(m)
H
, c = 1, . . . , N; m = 1, . . . , M
c
[ cos (
(m)
1
(m)
(z), c = 1, . . . , N
c
(m)
c
=
Ac
(m)
(m)
(m)
c
old
) – cos (
before and after frequency lock.
) – cos (
, which defines the coefficients of the comb filters, as
(m)
2
m
i
(m)
i
(m)
)] [ r cos (
)]
2
i
Multi-Component Tone Detection
opt
(m)
is found. From that point on,
new
) – cos (
. New filter coefficients
det
is reported by a
c
(m)
)]
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