AN2384 Freescale Semiconductor / Motorola, AN2384 Datasheet - Page 4

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

Multi-Component Tone Detection
An important case occurs when
Now the energy operator of x(n) becomes
Therefore, if multiple components have the same frequency but different gain and delay with respect to a given
reference component c, the energy operator of the x(n) signal is simply a scaled version of the energy operator of a
reference component. This result implies that the energy operator can handle multiple echoes of a single-frequency
tone.
The preferred approach to detecting multiple components using energy operators is first to filter the x(n) signal
with N independent filters so that every component x
extracted, their magnitude and frequency estimates (
case of a multi-component AM-FM demodulation [3], in which the magnitude (AM) and frequency (FM) of every
component is estimated, so that a tone is detected if these estimates are close enough to pre-defined reference
values. In general, the set of possible frequency combinations to be detected is given as follows:
This set then defines the following set of reference points for use by the detector:
Comb filters can efficiently decompose the signal so that a given filtering path (c) removes all the undesirable
components from the other paths (i
Where:
The following value is chosen:
So that this expression applies:
4
Generic Tone Detection Using Teager-Kaiser Energy Operators on the StarCore SC140 Core, Rev. 1
k
(x(n)) =
H
c
(m)
g
1
i
c
=
(z) =
(
c). The preferred filter structure has the general form:
and A
i=1
N
x
c
F = {(
R = {(
(m)
(n) = A
c
g
i
2
i
i
= g
+ 2
b
c
(m)
i
1
c
| H
(m)
(m)
1 – rb
i
1 – b
cos(n
A for all components, which then makes
t<s
1
= 2cos(
c
, . . . ,
, . . . ,
(m)
c
g
Ai
(n) can be extracted efficiently. Once the N components are
t
(m)
i
(m)
i
g
and
(m)
c
(e
c
s
z
+
j
cos (
N
z
(m)
(m)
–1
i
(m)
–1
c
N
), m = 1, . . . , M},
), m = 1, . . . , M},
(m)
c
+ z
), 0 <
), c = 1, . . ., N
+ r
i
) are computed. This problem is viewed as a special
t
)| = 1
–
–2
2
r
z
s
–2
< 1
)
)
, c = 1, . . . , N
k
(x
c
(n)), c = 1, . . . , N
Freescale Semiconductor
(.) independent of n.