Design of hybrid filter banks for analog/digital conversion
Design of hybrid filter banks for analog/digital conversion
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DOI：
10.1109/78.668549
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发表时间：
1998-04
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影响因子：
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通讯作者：
S. Velazquez;Truong Q. Nguyen;S. R. Broadstone
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文献类型：
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作者：
S. Velazquez;Truong Q. Nguyen;S. R. Broadstone
本文介绍了用于高速、高分辨率模数转换的混合滤波器组（HFB）的设计算法。HFB是一种非传统的滤波器组，采用模拟和数字滤波器。与低速转换器阵列结合使用时，与标准时间交错阵列转换技术相比，HFB可提高转换速度和分辨率。HFB中的模拟和数字滤波器必须设计为充分隔离通道，并且不会引入限制系统分辨率的重构误差。为了设计用于HFB的连续时间模拟滤波器，开发了离散时间到连续时间（“Z-to-S”）变换以将完美重构（PR）离散时间滤波器组转换为近PR HFB;开发了基于快速傅立叶变换（FFT）的计算高效算法以设计用于HFB的数字滤波器。设计了一个双通道HFB，采用六阶连续时间模拟滤波器和长度为64的FIR数字滤波器，平均混叠误差为-86 dB。为了设计离散时间模拟滤波器（例如，开关电容器或电荷耦合器件），使用PR离散时间滤波器组的无损因式分解，使得重构误差不受滤波器系数量化的影响。一个增益归一化技术的开发，以最大限度地提高动态范围的有限精度的实现。四通道HFB被设计为具有9位（整数）滤波器系数。当内部精度限制为15位时，最大混叠误差为-70 dB;当内部精度为20位时，最大混叠误差为-100 dB。9位滤波器系数使阻带衰减（与未量化系数相比）降低不到3 dB。
This paper presents design algorithms for hybrid filter banks (HFBs) for high-speed, high-resolution conversion between analog and digital signals. The HFB is an unconventional class of filter bank that employs both analog and digital filters. When used in conjunction with an array of slower speed converters, the HFB improves the speed and resolution of the conversion compared with the standard time-interleaved array conversion technique. The analog and digital filters in the HFB must be designed so that they adequately isolate the channels and do not introduce reconstruction errors that limit the resolution of the system. To design continuous-time analog filters for HFBs, a discrete-time-to-continuous-time ("Z-to-S") transform is developed to convert a perfect reconstruction (PR) discrete-time filter bank into a near-PR HFB; a computationally efficient algorithm based on the fast Fourier transform (FFT) is developed to design the digital filters for HFBs. A two-channel HFB is designed with sixth-order continuous-time analog filters and length 64 FIR digital filters that yield -86 dB average aliasing error. To design discrete-time analog filters (e.g., switched-capacitors or charge-coupled devices) for HFBs, a lossless factorization of a PR discrete-time filter bank is used so that the reconstruction error is not affected by filter coefficient quantization. A gain normalization technique is developed to maximize the dynamic range in the finite-precision implementation. A four-channel HFB is designed with 9-bit (integer) filter coefficients. With internal precision limited to the equivalent of 15 bits, the maximum aliasing error is -70 dB, and with the equivalent of 20 bits internal precision, maximum aliasing is -100 dB. The 9-bit filter coefficients degrade the stopband attenuation (compared with unquantized coefficients) by less than 3 dB.