Design of recursive 1-D variable filters with guaranteed stability
Design of recursive 1-D variable filters with guaranteed stability
复制标题
具有保证稳定性的递归一维变量滤波器的设计
DOI：
10.1109/82.624989
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发表时间：
1997
期刊：
影响因子：
--
通讯作者：
T. Deng
中科院分区：
文献类型：
--
作者：
T. Deng
具有可调频域特性的数字滤波器称为可变滤波器。变量滤波器在许多信号处理领域都有应用，但递归变量滤波器由于其稳定性问题，设计起来非常困难。本文提出了一种设计稳定性有保证的递归一维变量滤波器的新方法。该方法将变量数字滤波器的传递函数系数求为几个变量的多维多项式。这些变量表示不同的频域特性，因此，我们称这些变量为频谱参数。在应用所得到的变量滤波器时，将不同的谱参数值代入M-D多项式，将得到不同的滤波系数，从而得到不同的频域特性。为了保证稳定性，我们首先对分母系数进行系数替换，使其满足稳定性条件。然后将分母和分子系数确定为M-D多项式。在确定M-D多项式时，我们还提出了一种有效的最小二乘近似方法，该方法只需要求解联立线性方程。最后给出了两个算例，说明了所提出的可变滤波器设计技术的有效性。
The digital filters with adjustable frequency-domain characteristics are called variable filters. Variable filters are used in many signal processing fields, but the recursive variable filters are extremely difficult to design due to the stability problem. This paper proposes a new method for designing recursive one-dimensional (1-D) variable filters whose stability is guaranteed. The method finds the coefficients of the transfer function of a variable digital filter as the multidimensional (M-D) polynomials of a few variables. The variables specify different frequency-domain characteristics, thus, we call the variables the spectral parameters. In applying the resulting variable filters, substituting different values of the spectral parameters into the M-D polynomials will obtain different filter coefficients and, thus, obtain different frequency-domain characteristics. To guarantee the stability, we first perform coefficient substitutions on the denominator coefficients such that they satisfy the stability conditions. Then both denominator and numerator coefficients are determined as M-D polynomials. In determining the M-D polynomials, we also propose an efficient least-squares approximation method that requires only solving simultaneous linear equations. Two examples are given to show the effectiveness of the proposed variable filter design technique.