AN2384 Freescale Semiconductor / Motorola, AN2384 Datasheet - Page 3

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

A third order polynomial is selected for this task, so that
The coefficients are normalized to the range between –1 and +1, thus resulting in an additional three shifts (that is,
2
In practice, the x(n) signal is corrupted by noise. To overcome this practical constraint, a low pass filter (LPF) is
used to smoothen the outputs from the
single pole LPF of the following form:
If the detector is required to handle high noise levels, the outputs from the TK energy operators may also need to be
filtered.
2
When the x(n) signal is composed of more than one frequency, extending the preceding method is not so simple. In
this case,
so that
The function
components. It can be shown that
Freescale Semiconductor
b+1
changes to 2
Multi-Component Tone Detection
Generic Tone Detection Using Teager-Kaiser Energy Operators on the StarCore SC140 Core, Rev. 1
b+4
makes the energy operator time-varying, thus imposing additional difficulty in separating the N
). The normalized coefficients are listed in the following table:
n,
1
, . . .
N
) = 2
a
a
a
a
k
0
1
2
3
(x(n)) =
t<s
q = N (a
is given by
A
A
A(z) =
and
t
A
s
x(n) =
{sin
i=1
sin
3
N
+ D’(a
A
f(x) =
1 – az
2
i
2
1 – a
estimates. This noise reduction stage occurs efficiently through a
2
(k (
(k (
i=1
N
sin
-1
2x
2
A
1 ,
t
2
t
i
+ D’(a
+
–
cos(n
, 0 < a < 1
(k
–0.22482299804688
–0.73565673828125
s
1
2
0.66952514648438
0.35321044921875
s
) / 2) cos ((
) / 2) cos ((
i
) +
1
i + i
+ D’a
x 1.
)
(n,
0
))) 2
t
1,
t
+
–
b+4
. . .
s
s
) (n – k) +
) (n – k) +
N
)
Multi-Component Tone Detection
t
t
s
s
) +
) }
3