AN2832 Freescale Semiconductor / Motorola, AN2832 Datasheet - Page 8

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

Remote Diagnostic Architecture
When the receive frame is obtained, it is used to compute the average, that is, the low-pass filter (LPF), of the
receive signal (y(n)). In this computation, the receive samples from at least the first two frames and the last two
frames are usually ignored due to boundary effects of the linear convolution and do not represent valid circular
convolution.
2.4 Calculating the Impulse Response
To find the frequency response of the hybrid impulse response, the discrete Fourier transforms of x(n) and y(n)
must be computed (that is, X and Y). A standard code for computing these transforms via FFTs is available in [8],
but optimized libraries for StarCore DSP cores are freely available on the Freescale Semiconductor website listed
on the back cover of this document. The H
magnitude of the training signal x(n) frequency response is 1 (that is, |X| = 1), dividing by X is the same as
multiplying by its complex conjugate. Calculating the frequency response this way eliminates costly division
operations and therefore is the method used in the code. The h
the inverse discrete Fourier transform of the H
2.5 Emulating Target Impulse Responses
As discussed in Section 1, after a physical hybrid impulse response is estimated, you can selectively emulate
another hybrid circuit by compensating the existing echo and then injecting a desired echo signal. As Figure 4
shows, a target impulse response h
estimate of the physical hybrid circuit impulse response. In this process, h
necessarily time-invariant. This method was validated in real time with a carrier-class network echo canceller using
different target impulse responses.
2.6 Considerations for Real-Time Implementation
Implementing FFT-based channel estimation in real time requires careful control of other modules, such as the
ECAN. As described in Section 2.2, during the training phase, the ECAN must be disabled and r
suppressed. The following algorithm summarizes the resulting steps:
8
1.
2.
For every channel, generate a zero-mean, white Gaussian noise training signal x(n) using the following
equation:
where the Φ
between 0 and 2π. (Φ
r
the training period (M ⋅ N samples), regardless of the spectrum of r
Periodically transmit x(n), read the receive signal y(n), and compute the averaged receive signal y(n),
that is, a low-pass filtered version of y(n).
The x(n) signal is transmitted periodically so that the receive signal y(n) is a circular convolution with
the channel impulse response h. This allows use of point-by-point multiplication of discrete Fourier
transforms (DFTs) in step 4 to obtain the frequency response of the channel. During the training, the
0
(n) in Figure 4 so that the resulting spectrum of x(n) is flat (that is, unit gain per frequency) during
Packet Telephony Remote Diagnostics on the StarCore SC140 Core, Rev. 1
x n ( )
k
are independent, identically distributed random variables having uniform distribution
=
1
----------------------
k
+
t
(n) is easily emulated by defining z(n) = (h
~ U(0,2π), ∀
– ( )
N
1
n
est
+
frequency response is the result of dividing Y by X. Because the
--- -
N
2
est
⋅
k
frequency response.
). The r
N
--- - 1
k
2
∑
=
–
1
cos
0
(n) receive signal is suppressed by setting r(n) = x(n) –
⎛
⎝
2π kn
---------------- -
est
N
⋅
impulse response estimate is then found by taking
+
Φ
k
⎞ ,
⎠
t
(n) can be any linear filter, not
t
(n) – h
0
(n).
n
=
est
0 1 . . .
) * r
, ,
Freescale Semiconductor
0
(n), where h
0
N 1
(n) must be
–
Equation 7
est
is the