AI 中文总结
该研究提出基于FFT的循环逆PFB算法，结合维纳滤波和最大似然重构缓解量化噪声，可实现存档PFB数据的高分辨率光谱分析，服务于射电天文等应用。
AI 中文摘要
多相滤波器组（PFB）被广泛用于实时信道化数字化时域数据。然而，射电天文等应用常需要高于实时系统所能提供的光谱分辨率。我们提出一种循环逆PFB形式化方法，并给出一种基于快速傅里叶变换（FFT）的可扩展新算法，用于对临界采样PFB进行逆变换。该形式化方法明确识别量化噪声放大的来源，并支持两种互补的缓解策略：（1）一种快速实用的维纳滤波器；（2）一种结合时域先验的严格最大似然重构。我们使用模拟的4比特量化PFB数据评估这两种方法。对于自谱，维纳滤波将重构误差限制在信道宽度的10%以内，峰值误差低于10%。当纳入额外的时域先验信息时，最大似然方法可进一步降低重构误差，当先验覆盖10%的时域样本时，最坏情况下的误差可降至2%以下。该框架可实现对存档PFB数据的高分辨率光谱分析，为长基线干涉测量、脉冲星与快速射电暴搜索以及超窄带物理实验等应用提供便利。
英文摘要
Polyphase filter banks (PFBs) are widely used to channelize digitized time-domain data in real time. However, applications such as radio astronomy often require higher spectral resolution than real-time systems can provide. We introduce a circulant inverse-PFB formalism and present a new, scalable, fast Fourier transform (FFT)-based algorithm for inverting critically sampled PFBs. This formalism explicitly identifies the origin of quantization noise amplification and enables two complementary mitigation strategies: (1) a fast, practical Wiener filter and (2) a rigorous maximum-likelihood reconstruction with time-domain priors. We evaluate both approaches using simulated 4-bit quantized PFB data. For autospectra, Wiener filtering confines reconstruction errors to less than 10\% of the channel width, with a peak error below 10\%. The maximum-likelihood approach further reduces reconstruction errors as additional time-domain prior information is incorporated, with priors spanning 10\% of the time-domain samples reducing worst-case errors to below 2\%. This framework enables high-resolution spectral analysis of archival PFB data, facilitating applications including long-baseline interferometry, pulsar and fast radio burst searches, and ultra-narrow-band physics experiments.
