AN2832 Freescale Semiconductor / Motorola, AN2832 Datasheet - Page 7

• Manufacturer Part Number: AN2832
• Description: Packet Telephony Remote Diagnostics on the StarCore SC140 Core
• Manufacturer: Freescale Semiconductor / Motorola

Obtaining the Φ
numbers can be found in [8]. This reference provides a number of random number generators, from which uniform
and identically distributed random variables are easily generated. The values for Φ
they are transformed as follows:
such that l
recurrence method is an efficient way to calculate cosines, as shown in Equation 4.
and n = 0, 1, . . . , N – 1, and c(n) and s(n) represent the discrete cosine and discrete sine, respectively. Solving
Equation 4 for c(n) results in the well-known digital oscillator [9].
Using the initial conditions c(0) = 1 and c(1) = cosθ, all other values of cosine for n = 0, 1, . . . N – 1 can be
computed efficiently. Due to the even symmetry of the cosine function, only half of these values (that is, n = 0, 1, .
. . , N / 2 – 1) are computed and stored in a look-up table for future reference. The values from this look-up table are
then used in the following cosine computation:
The look-up table is accessed via modular addressing, and the evenness or oddness of the remainder of (kn + l
(N / 2) indicates whether the positive or negative value of the cosine is used. An even remainder indicates the
positive value of the cosine, and an odd remainder indicates the negative value. Therefore, the training signal x(n)
is composed by simple superposition of scaled discrete cosine values taken from a look-up table of c(n), n = 0, 1, .
. . , N / 2 – 1.
2.3 Transmitting the Training Signal
After the training signal x(n) is generated, it is periodically transmitted across the channel through the hybrid, and
the average of the receive signal (echo signal + noise) is computed. N samples of the transmit signal x(n) make up
one transmit frame, and a user-specified number of frames (M) determines how many times the signal is repeatedly
transmitted. The buffer storing the signal is accessed circularly. Multiple transmissions of the same data frame are
important for mitigating spurious noise and improving estimation accuracy.
Freescale Semiconductor
k
is a discrete, uniformly distributed random variable with values 0,1, . . . ,N–1. The rotation matrix
k
values requires the use of a random number generator. A standard code to generate random
Packet Telephony Remote Diagnostics on the StarCore SC140 Core, Rev. 1
cos
cos
sin
⎛
⎝
2π k n
-------------------- -
θ
θ
⋅ ⋅
N
–
cos
c n ( )
+
sin
Φ
cos
θ
θ
k
⎞
⎠
=
⋅
2π
----- - kn
=
N
2
c n 1
s n 1
⋅
cos
(
(
(
cos
–
–
+
2π
----- - kn
θ
N
l
)
)
⋅
k
(
c n 1
)
=
(
=
+
–
c n ( )
s n ( )
c kn
l
k
(
) c n 2
)
–
, where l
,
+
(
l
k
–
)
where θ
)
k
=
k
----- - Φ
2π
Remote Diagnostic Architecture
N
vary between 0 and 2π, but
=
⋅
2π
----- -
N
k
Equation 3
Equation 4
Equation 5
Equation 6
k
) /
7