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p(l)x(n l) + u(n) + v(n).
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By making the length of W (z) suf ciently long, the residual echo can be minimized. However, as discussed in Section 7.3.3, the excess mean-square error (MSE) produced by the adaptive algorithm and nite-precision errors are also proportional to the lter length. Therefore, there is an optimum length L for echo cancelation. The number of coef cients required for the FIR lter is determined by the tail delay. As mentioned earlier, the impulse response of the hybrid (dispersive delay) is relatively short. However, the at delay from the echo canceler to the hybrid depends on the physical location of the echo canceler, and the processing delay of transmission equipments.
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10.2.2 Performance Evaluation
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The effectiveness of an echo canceler is usually measured by the echo return loss enhancement (ERLE) de ned as ERLE = 10 log E d 2 (n) E e2 (n) . (10.5)
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For a given application, the ERLE depends on the step size , the lter length L, the signal-to-noise ratio, and the nature of signal in terms of power and spectral contents. A larger step size provides a faster initial convergence, but the nal ERLE is smaller due to the excess MSE and quantization errors. If the lter length is long enough to cover the length of echo tail, increasing L will further reduce the ERLE. The ERLE achieved by an echo canceler is limited by many practical factors. Detailed requirements of an adaptive echo canceler are de ned by ITU-T Recommendations G.165 and G.168, including the maximum residual echo level, the echo suppression effect on the hybrid, the convergence time, the initial setup time, and the degradation in a double-talk situation. The rst special-purpose chip for echo cancelation implements a single 128-tap adaptive echo canceler [5]. In the past, adaptive echo cancelers were implemented using customized devices in order to handle the heavy computation in real-time applications. Disadvantages of VLSI (very large scale integrated circuit) implementation are long development time, high development cost, and lack of exibility to meet application-speci c requirements and improvements such as the standard changed from G.165 to G.168. Therefore, recent activities in the design and implementation of adaptive echo cancelers for real-world applications are focus on programmable DSP processors.
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10.3 Practical Considerations
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This section discusses two practical techniques in designing adaptive echo canceler: prewhitening and delay detection.
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10.3.1 Prewhitening of Signals
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As discussed in 7, convergence time of adaptive FIR lter with the LMS algorithm is proportional to spectral ratio max / min . Thus, an input signal with at spectrum such as white noise has faster convergence rate. Since speech signal is highly correlated with non at spectrum, the convergence speed is slow. The decorrelation (whitening) of input signal will improve the convergence speed. Figure 10.6 shows a typical prewhitening structure for input signals. The whitening lter FW (z) is used for both the far-end and near-end signals. This xed lter could be obtained using the reversed statistical or temporal averaged spectrum values. One example is the anti-tile lter used to lift up the high-frequency components since most speech signal s power is concentrated at the low-frequency region.
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d(n) y(n)
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FW(z) Echo path W(z)
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Block diagram of a signal prewhitening structure
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Block diagram of an adaptive prewhitening structure
The whitening lter can be adaptive based on the far-end signal x(n). In this case, the lter coef cients update is synchronized for both branches. An equivalent structure of adaptive prewhitening is shown in Figure 10.7. The adaptation of the whitening lter coef cients is similar to a perceptive weighting lter, which will be discussed in 11. We can use the Levinson Durbin algorithm to estimate the input signal spectrum envelope and use the reversed function to lter the signal. The calculation of transfer function FW (z) is similar to the adaptive channel equalization discussed in 7. However, two conditions must be satis ed: the processing should be linear and the lter FW (z) must be reversible.