AN2832 Freescale Semiconductor / Motorola, AN2832 Datasheet - Page 6

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

Remote Diagnostic Architecture
2.1 Estimating the FFT-Based Hybrid Circuit Impulse Response
The impulse response of hybrid circuits is estimated with an FFT-based channel identification scheme similar to
the method used in ADSL systems, as shown in Figure 5.
2.2 Generating the Training Signal
The training signal is generated by a white Gaussian noise signal x(n) that is a function of uniformly distributed
random variables Φ
Converting this signal into the time domain by taking the inverse discrete Fourier transform results in the signal
shown in Equation 2.
where N is the period of the training signal. This real-valued signal is generated in the code. Notice that this
training signal is obtained by setting r(n) = x(n) – r
adjusted to a convenient power level. This signal is generated on the basis of the two main parts of the equation: a
method for efficiently computing cosines and a random number generator to produce the random phases:
6
y(n)
x(n)
Transmitter
Serial to
Periodic
Parallel
Control
Figure 5. FFT-Based Structure for Estimating Hybrid Circuit Impulse Responses
x n ( )
X k ( )
k
’s in the frequency domain, as shown in Equation 1.
Packet Telephony Remote Diagnostics on the StarCore SC140 Core, Rev. 1
=
=
1
----------------------
e
j Φ
+
⋅
(
N
1 –
k
,
k
)
n
=
Parallel to
Low-Pass
+
Serial
1 ...,
Filter
--- -
N
,
2
Φ
⋅
N
--- - 1
k
2
k
∑
N
--- - 1
2
=
,
–
1
– , where Φ
cos
0
(n) (see Figure 4). Before transmission, the signal can be
⎛
⎝
y(n)
k
2π kn
---------------- -
= , . . . ,
N
⋅
1
Fast Fourier
Fast Fourier
Inverse 1-D
Transform
Transform
o
+
=
Φ
N
--- - 1
Φ
2
k
⎞ ,
⎠
N 2 ⁄
–
=
Y
0 and X
n
=
Conjugate
Complex
X*
0 1 . . ,
X
, ,
X
k
=
X
N 1
Freescale Semiconductor
*
N k
–
–
h
Fast Fourier
Inverse 1-D
Transform
est
+
Equation 1
Equation 2
h(n)
–
h
eff
(n)