A simple derivation of the spectral transformations for IIR filters

Roy S.C.D.

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A simple derivation of the spectral transformations for IIR filters

机译：IIR滤波器的光谱变换的简单推导

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摘要

A simple method is given for deriving the spectral transformations for infinite-impulse response (IIR) filters, which can be used to transform a prototype low-pass (LP) digital filter to another LP, high-pass (HP), bandpass (BP), or band-stop (BS) digital filter with prescribed passband edge(s) and the same tolerances as those of the prototype. The method is based on a combination of bilinear transformation with the analog frequency transformation and is simpler-conceptually, as well as from the calculation point of view-than the conventional method based on all-pass transformation functions.

机译：给出了一种简单的方法来推导无限脉冲响应（IIR）滤波器的频谱变换，该方法可用于将原型低通（LP）数字滤波器变换为另一个LP，高通（HP）带通（BP））或具有规定通带边沿并具有与原型相同的公差的带阻（BS）数字滤波器。与基于全通变换函数的传统方法相比，该方法基于双线性变换与模拟频率变换的组合，并且从概念上以及从计算角度来看都更简单。

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《IEEE Transactions on Education》 |2005年第2期|p.274-278|共5页
作者
Roy S.C.D.;
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正文语种 eng
中图分类电工技术;
关键词
IIR filters; band-pass filters; high-pass filters; low-pass filters; IIR filter; analog frequency transformation; bilinear transformation; digital filter; infinite impulse response filter; spectral transformation; Digital filters; digital signal processing; infinite;

机译：IIR滤波器;带通滤波器;高通滤波器;低通滤波器;IIR滤波器;模拟频率变换;双线性变换;数字滤波器;无限冲激响应滤波器;频谱变换;数字滤波器;数字信号处理;无限;

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专利

1. New General Transformations for 2-D FIR and IIR Filters' Design [J] . NIKOS E. MASTORAKIS WSEAS Transactions on Circuits and Systems . 2011,第1a3期

机译：二维FIR和IIR滤波器设计的新通用转换
2. Improved design of causal stable IIR perfect reconstruction filter banks using transformations of variables [J] . Tay D.B.H. Electronics Letters . 1997,第7期

机译：使用变量变换改进因果稳定IIR完美重构滤波器组的设计
3. Pipelined adaptive IIR filter architectures using scattered and relaxed look-ahead transformations [J] . Shanbhag N.R., Gi-Hong Im IEEE Transactions on Signal Processing . 1996,第7期

机译：使用分散和宽松的前瞻性转换的流水线式自适应IIR滤波器架构
4. Design of three-dimensional spherically symmetric IIR digital filters with real and complex coefficients using spectral transformations [C] . Sekiguchi, T., Takahashi, . 1989

机译：利用频谱变换设计具有实系数和复系数的三维球对称IIR数字滤波器
5. Multispectral MWIR image classification using filters derived from independent component analysis. [D] . Chari, Srikant. 2007

机译：多光谱MWIR图像分类，使用独立分量分析得出的滤波器。
6. Functional transformation of Fourier-transform mid-infrared spectrum for improving spectral specificity by simple algorithm based on wavelet-like functions [O] . Manuel Palencia 2018

机译：利用基于小波函数的简单算法对傅立叶变换中红外光谱进行功能变换以提高光谱特异性
7. The design and implementation of a digital infinite impulse response (IIR) Lowpass Butterworth filter– impulse response (IIR) Lowpass Butterworth filter– A comparison of Matlab and Bilinear transformation methods [O] . B. J. Kwaha 2011

机译：数字无限脉冲响应的设计与实现（IIR）Lowpass Butterworth滤波 - 脉冲响应（IIR）Lowpass Butterworth滤波器 - Matlab和Bilinear转化方法的比较
8. Derivation of the First Order Transformation Matrix for a Simple Wien Filter and Comparison to Results of Numerical Integration [R] . Hurd, J. V. 1986

机译：简单Wien滤波器一阶变换矩阵的推导及与数值积分结果的比较

A simple derivation of the spectral transformations for IIR filters

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