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Abstract Nabil Roneh Yousef Effect of Finite Wordlength on the Performance of Adaptive Filters. Master of Science dissertation, Ain Shams University, 1997. In adaptive filtering applications dealing with high speed data communications, the baud interval may not be long enough to enable the execution of one iteration of the adaptive filter coefficients according to the conventional least mean square (LMS) algorithm. This has initiated the need of multiplication-free adaptive digital signal processing algorithms. These algorithms include the signed regressor algorithm (SRA) and the sign algorithm (SA). The analyses of these algorithms are available only for the infinite precision implementation of the algorithms. However, in digital implementation, signals and adaptive filter coefficients are quantized to finite· wordlengths. This results in a steady state excess quantization error at the output of the adaptive filter. This error has not yet been analyzed in literature. The present thesis has four main contributions inthis context. In the first contribution, the thesis provides roundoff error analyses of the SRA and the SA in a stationary environment with Gaussian data. Expressions are derived for the steady state excess quantization mean square error of both algorithms. It is shown that the steady state excess quantization mean square error is a decreasing function of both the filter coefficients and data wordlengths. For both algorithms, it is found that there exists an optimum step size that minimizes the excess quantization mean square error. Expressions for this optimum step size are derived for each algorithm. The second contribution is the study of the transient behavior of the SRA, and the SA. Expressions for the convergence times of the algorithms are derived. It is found that effects of roundoff errors are minor at the beginning of convergence and they become effective only when the algorithm approaches its steady state. In the third contribution, the thesis analyzes the adaptation stopping and slow-down phenomena in the SRA and the SA. It is found that stopping takes place in the SRA when data and noise have bounded .. ABSTRACT Nabil Roneh Yousef Effect of Finite Wordlength on the Performance of Adaptive Filters. Master of Science dissertation, Ain Shams University, 1997. In adaptive filtering applications dealing with high speed data communications, the baud interval may not be long enough to enable the execution of one iteration of the adaptive filter coefficients according to the conventional least mean square (LMS) algorithm. This has initiated the need of multiplication-free adaptive digital signal processing algorithms. These algorithms include the signed regressor algorithm (SRA) and the sign algorithm (SA). The analyses of these algorithms are available only for the infinite precision implementation of the algorithms. However, in digital implementation, signals and adaptive filter coefficients are quantized to finite· wordlengths. This results in a steady state excess quantization error at the output of the adaptive filter. This error has not yet been analyzed in literature. The present thesis has four main contributions inthis context. In the first contribution, the thesis provides roundoff error analyses of the SRA and the SA in a stationary environment with Gaussian data. Expressions are derived for the steady state excess quantization mean square error of both algorithms. It is shown that the steady state excess quantization mean square error is a decreasing function of both the filter coefficients and data wordlengths. For both algorithms, it is found that there exists an optimum step size that minimizes the excess quantization mean square error. Expressions for this optimum step size are derived for each algorithm. The second contribution is the study of the transient behavior of the SRA, and the SA. Expressions for the convergence times of the algorithms are derived. It is found that effects of roundoff errors are minor at the beginning of convergence and they become effective only when the algorithm approaches its steady state. In the third contribution, the thesis analyzes the adaptation stopping and slow-down phenomena in the SRA and the SA. It is found that stopping takes place in the SRA when data and noise have bounded distributions such as the uniform distnbution, while the slow-down takes place when they follow unbounded distributions, such as the Gaussian distribution. Surprisingly, it is found that neither stopping nor slow-down takes place in the case of the SA. The fourth contribution is the proposal of an algorithm that reduces the effect of finite wordlength on the performance of the adaptive filter. Expressions are derived for the steady state mean square error and the convergence time of the proposed algorithm. It is found that the proposed algorithm possesses higher resistance to roundoff errors than that of the conventional algorithm. The analytical findings of the thesis are supported by computer simulations. |