We develop characteristics-based filter 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 are useful for seismic signal phase-picking, cochlear implants, and equalizers. The native frequency-domain specifications for GEFs are not on given frequency responses but rather on filter characteristics such as peak frequency, bandwidth, and group delay. Our characteristics-based method for filter design accommodates direct specification of a trio of frequency-domain characteristics from amongst the peak frequency, convexity, ndB quality factors, equivalent rectangular bandwidth, maximum group delay, and phase accumulation. We achieve this by deriving filter parameterizations with 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 ones with simultaneous specification of magnitude-based and phase-based characteristics (e.g. bandwidths and group delays). This in turn enables designing sharply tuned filters without significant group delay, and simultaneous control over frequency selectivity and synchronization which is important in designing filterbanks. Our filter design methods with direct control over characteristics may also be utilized beyond static filter design 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, simple, and computationally efficient. The methods extend to the design of related bandpass and multiband filters.

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，GEFs）开发了基于特性的滤波器设计方法，该类滤波器可表示为二阶滤波器提升至非单位指数的形式。GEFs具有峰值特性、近似线性相位，适用于地震信号相位拾取、人工耳蜗及均衡器等应用。GEFs的固有频域指标并非直接给定频率响应，而是基于滤波器特性，如峰值频率、带宽和群延迟。我们提出的基于特性的滤波器设计方法支持从峰值频率、凸度、ndB品质因数、等效矩形带宽、最大群延迟及相位累积等特性中直接指定一组三重频域特性。通过建立滤波器特性集与滤波器参数的映射关系实现这一目标，具体方法为：利用锐化滤波器近似，推导出将滤波器特性集映射至原始滤波器常数的闭式解析表达式。由此得到GEFs的参数化模型，包括可同时指定幅值特性与相位特性（如带宽与群延迟）的模型。这使得设计具有低群延迟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，这对滤波器组设计至关重要。我们这种可直接控制特性的滤波器设计方法不仅适用于静态滤波器设计，还可扩展至高阶可变带通滤波器设计，并有望用于基于特性的自适应滤波。该方法具有固有稳定性、满足严格特性指标的高精度、简单性和计算高效性等特点，并可进一步推广至相关带通及多带滤波器的设计。