| Summary: | 博士 === 國立交通大學 === 電信工程研究所 === 86 === Adaptive autoregressive (AR) modeling is widely used in
signal processingIt is well-known that the coefficients of an AR
model can be easily obtained using an LMS prediction error
filter. However, this filter givesa biased solution when the
input signal is corrupted by additive white noise.In this
thesis, we propose a new class of adaptive filter to solve the
problem. This class of filters, known as the ρ-LMS filter,
is derived fromthe estimation theory. The main idea is to filter
the noisy input and error signal and then use the results in
the LMS algorithm. Since the noise level is reduced, the bias
problem will consequently be reduced. The ρ-LMS filter is
linear when the noise is Gaussian, however, it becomes
nonlinear when the noise is non-Gaussian. Since the general
non-Gaussian filtering is difficult, we only consider the case
where the noise distribution can be approximated by a Gaussian
sum. Theoretical analysis of the first- and second-order
statistics for the linear and nonlinear ρ-LMS filters are
also presented. A fast algorithm derived from the Newton method
is developed to accelerate the convergence rate of ρ-LMS
filters. This leads to the fast ρ-LMS-Newton filters. Asa by-
product, the ρ-LMS filter can output filtered results. This is
animportant property not shared by other LMS-type filters. In
other words,AR modeling and filtering are combined in a single
filter. The linear ρ-LMS filter can act like a Kalman filter
when noise is Gaussian, and the nonlinear ρ-LMS filter can act
like a Masreliez''s filter when noise isnon-Gaussian. The
proposed filters are then applied in line enhancement and active
noise cancellation and satisfactory results are observed. As far
asfiltering concern, there is another way to deal with the bias
problem. We canuse a biased driving noise variance to compensate
for the effect caused by the biased AR coefficients. When the AR
order is low, this approach can yield a good suboptimal result.
We use this method in speech enhancement.Noisy speech is first
decomposed into subbbands. Subband signals are then modeled as
low-order AR process, such that low-order Kalman filter can be
applied to enhance subband signals. Enhanced subband signals are
finallycombined to form the enhanced fullband speech. To
identify AR coefficients,the conventional prediction-error
filters are used. The performance ofthe Kalman filter with
biased parameters is analyzed. This approach not only greatly
reduces the computational complexity, but also achieves good
performance.
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