Closed-form design and efficient implementation of variable digital filters with simultaneously tunable magnitude and fractional delay
Closed-form design and efficient implementation of variable digital filters with simultaneously tunable magnitude and fractional delay
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DOI：
10.1109/tsp.2004.827150
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发表时间：
2004-06
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
本文提出了一种封闭形式的解决方案，设计可变的一维（1-D）有限脉冲响应（FIR）数字滤波器，同时可调幅度和可调分数相位延迟响应。首先，可变FIR滤波器的每个系数被表示为一对称为谱参数的参数的二维（2-D）多项式;一个用于独立调谐幅度响应的截止频率，另一个用于独立调谐分数相位延迟。然后，在不离散任何设计参数，如频率和两个频谱参数之间的期望和实际的可变频率响应的封闭形式的误差函数导出。最后，二维多项式系数的最优解可以很容易地通过最小化封闭形式的误差函数来确定。我们还表明，由此产生的可变FIR滤波器可以有效地实现推广法罗结构，我们的两个参数的情况下。广义Farrow结构只需要少量的乘法和加法就可以获得任何新的频率特性，这特别适合于高速调谐。
This paper proposes a closed-form solution for designing variable one-dimensional (1-D) finite-impulse-response (FIR) digital filters with simultaneously tunable magnitude and tunable fractional phase-delay responses. First, each coefficient of a variable FIR filter is expressed as a two-dimensional (2-D) polynomial of a pair of parameters called spectral parameters; one is for independently tuning the cutoff frequency of the magnitude response, and the other is for independently tuning fractional phase-delay. Then, the closed-form error function between the desired and actual variable frequency responses is derived without discretizing any design parameters such as the frequency and the two spectral parameters. Finally, the optimal solution for the 2-D polynomial coefficients can be easily determined through minimizing the closed-form error function. We also show that the resulting variable FIR filter can be efficiently implemented by generalizing Farrow structure to our two-parameter case. The generalized Farrow structure requires only a small number of multiplications and additions for obtaining any new frequency characteristic, which is particularly suitable for high-speed tuning.