We develop characteristics-based design methods for a class of IIR bandpass filters which we refer to as Generalized Exponent Filters (GEFs) and that are represented as second order filters raised to non-unitary exponents. GEFs have a peak, are effectively linear phase, and may be used for phase-picking for seismic signals, cochlear implants, rainbow sensors, and equalizers. The native specifications for GEFs are not on a given frequency response but rather on filter characteristics such as peak frequency, quality factor, and group delay. Our characteristics-based method for design accommodates direct specification of a trio of frequency-domain characteristics from amongst the peak frequency, 3dB quality factor, equivalent rectangular bandwidth, maximum group delay, and phase accumulation. We achieve this by deriving parameterizations for the filters in terms of sets of filter characteristics which involves deriving closed-form analytic expressions mapping sets of filter characteristics to the original filter constants by making sharp-filter approximations. This results in parameterizations for GEFs including mixed parameterizations based on simultaneous specification of magnitude-based characteristics (e.g. bandwidths) and phase-based characteristics (e.g. group delays) which enables designing sharply tuned filters without significant group delay and simultaneous control over frequency selectivity and synchronization which is important in designing filterbanks. Our design methods with direct control over characteristics may also be utilized for higher-order variable bandpass filter design and may be useful for characteristics-based adaptive filtering. Our methods are inherently stable, highly accurate in meeting strict specifications on desired characteristics, and computationally efficient. The methods extend to the design of related bandpass, multiband filters, and filterbanks.

翻译：本文针对一类IIR带通滤波器（我们称之为广义指数滤波器，GEF）提出了基于特性的设计方法，这类滤波器表示为二阶滤波器提升至非单位指数的形式。GEF具有峰值特性、近似线性相位，可应用于地震信号相位拾取、人工耳蜗、彩虹传感器及均衡器等领域。GEF的原始设计规范并非基于给定的频率响应，而是基于滤波器特性参数，如峰值频率、品质因数与群时延。我们提出的基于特性的设计方法支持从峰值频率、3dB品质因数、等效矩形带宽、最大群时延及相位累积量这五个频域特性中直接指定三个特性参数进行设计。通过建立滤波器特性集合的参数化模型，并借助锐化滤波器近似推导滤波器特性集合到原始滤波器常数的闭式解析映射关系，实现了这一目标。由此得到的GEF参数化模型包含基于幅值特性（如带宽）与相位特性（如群时延）混合指定的参数化方案，使得设计具有低群时延的锐调谐滤波器成为可能，并能同时控制频率选择性与同步性——这在滤波器组设计中至关重要。这种可直接调控特性的设计方法同样适用于高阶可变带通滤波器设计，并有望应用于基于特性的自适应滤波。所提方法具有固有稳定性、满足严格特性规范的高精度性及计算高效性。该方法可进一步扩展至相关带通滤波器、多带滤波器及滤波器组的设计。