AN2384 Freescale Semiconductor / Motorola, AN2384 Datasheet - Page 2

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

Tone Detection Basics
1
The design of the generic tone detector discussed in this document is based on the fact that any single-frequency
tone x(n) = A cos( n +
The modified TK energy operator is a special case of a Volterra filter, which depends both on the magnitude A and
the normalized frequency
frequency. Observe that
processing (k = 1 in the original definition of the TK algorithm); notice that the effect of applying
sampling rate ƒ
interest, sub-rate processing is a preferred approach because it reduces computational requirements.
Depending on the power of the signal (that is, the magnitude A of the tone), the energy operator generates different
levels for the same normalized frequency . Therefore, to estimate , you must efficiently remove this magnitude
dependency by, for example, processing x(n) through an FIR filter of the form B(z) = (z
applying the energy operator to the result. Once the dependency is removed,
computing the following ratio (
This expression derives from the definition of energy operators and the following trigonometric identity:
Therefore, selecting k = (l – m) / 2, the tone magnitude A is estimated by computing the following ratio (
Notice that
An important practical issue is how to compute the two divisions that estimate
approximation is employed according to the following approach for computing a ratio between a numerator N and
a denominator D:
D’ = D2
bits of the normalization (efficiently computed on most DSPs), and p(.) is a polynomial approximation of the
following function:
2
Tone Detection Basics
b
Generic Tone Detection Using Teager-Kaiser Energy Operators on the StarCore SC140 Core, Rev. 1
is the denominator normalized to the range between 1/2 and 1, b is the corresponding number of leading
A
/ 2 can be used to estimate the standard average power of x(n):
s
is equivalent to applying
k
is mapped to a constant value via the modified TK energy operator [1], as follows:
(x(n)) does not depend on the phase . The parameter k defines the underlying sub-rate
2
1
q =
of the tone;
=
[
cos (
N =
D
k
) of energy operators[2]:
k
(
(x(n)) = x
2
1
2N =
2D
(x(n – l) + x(n – m))
cos (
2
k
(n – k) – x(n)x(n – 2k) = A
2D
at a sampling rate ƒ
A
ƒ / ƒ
2N
(x(n))
b
=
2
–b
s
1 –
, where ƒ is the tone frequency and ƒ
k
= N
]
(x(n))
)
cos
( )
= A
( )
2D2
= cos
1
2
s
b
–
2
/ k. Depending on the range of frequencies of
2
2
2
b+1
sin
(
cos
( )
2
(k
(
= Np(D’)2
l – m
is indirectly estimated by
A
2
and
+
2
–l
)
b+1
)
+ z
efficiently. A polynomial
Freescale Semiconductor
s
–m
is the sampling
) / 2 and then
k
at a
A
) [2].