摘要翻译：
演化谱的复解调被描述为时频域的二维核平滑器。在第一阶段，计算一个锥形傅里叶变换$Y_{nu}（f,t)$。其次，平滑了对数谱估计$\hat{\theta}_{\nu}（f,t)\equiv\ln(y_{nu}（f,t)^2$。随着核平滑器特征宽度的增加，时间平均和频率平均的偏差增大，方差减小。解调参数，如谱锥度和核平滑器的阶数、长度和带宽，是通过最小化期望误差来确定的。对于分辨率较高的演化谱，最优锥度长度是最优核半宽的一小部分。光谱窗口的最佳频带宽度$W$为$W^2\约\lambda_f/\tau$,其中$\tau$为特征时间，$\lambda_f$为特征频率尺度长度。与此相反，第二阶段核平滑器的最优半宽度为$h\约1/(\tau\lambda_f)^{1\over(P+2)}$，其中$p$是核平滑器的顺序。最佳频率半宽与最佳时间半宽的比值满足$h_f/h_T~(\partial_t^p\theta/\partial_f^p\theta)$。由于期望损失依赖于未知的演化谱，我们首先用高阶核平滑器估计$\partial_t^p\theta^2$和$\partial_f^p\theta^2$,然后将估计的导数代入期望损失准则。
---
英文标题：
《Optimal Data-based Kernel Estimation of Evolutionary Spectra》
---
作者：
Kurt S. Riedel
---
最新提交年份：
2018
---
分类信息：

一级分类：Statistics        统计学
二级分类：Methodology        方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
--
一级分类：Electrical Engineering and Systems Science        电气工程与系统科学
二级分类：Audio and Speech Processing        音频和语音处理
分类描述：Theory and methods for processing signals representing audio, speech, and language, and their applications. This includes analysis, synthesis, enhancement, transformation, classification and interpretation of such signals as well as the design, development, and evaluation of associated signal processing systems. Machine learning and pattern analysis applied to any of the above areas is also welcome.  Specific topics of interest include: auditory modeling and hearing aids; acoustic beamforming and source localization; classification of acoustic scenes; speaker separation; active noise control and echo cancellation; enhancement; de-reverberation; bioacoustics; music signals analysis, synthesis and modification; music information retrieval;  audio for multimedia and joint audio-video processing; spoken and written language modeling, segmentation, tagging, parsing, understanding, and translation; text mining; speech production, perception, and psychoacoustics; speech analysis, synthesis, and perceptual modeling and coding; robust speech recognition; speaker recognition and characterization; deep learning, online learning, and graphical models applied to speech, audio, and language signals; and implementation aspects ranging from system architecture to fast algorithms.
处理代表音频、语音和语言的信号的理论和方法及其应用。这包括分析、合成、增强、转换、分类和解释这些信号，以及相关信号处理系统的设计、开发和评估。机器学习和模式分析应用于上述任何领域也是受欢迎的。感兴趣的具体主题包括：听觉建模和助听器；声波束形成与声源定位；声场景分类；说话人分离；有源噪声控制和回声消除；增强；去混响；生物声学；音乐信号的分析、合成与修饰；音乐信息检索；多媒体音频和联合音视频处理；口语和书面语建模、切分、标注、句法分析、理解和翻译；文本挖掘；言语产生、感知和心理声学；语音分析、合成、感知建模和编码；鲁棒语音识别；说话人识别与特征描述；应用于语音、音频和语言信号的深度学习、在线学习和图形模型；以及从系统架构到快速算法的实现方面。
--
一级分类：Electrical Engineering and Systems Science        电气工程与系统科学
二级分类：Image and Video Processing        图像和视频处理
分类描述：Theory, algorithms, and architectures for the formation, capture, processing, communication, analysis, and display of images, video, and multidimensional signals in a wide variety of applications. Topics of interest include: mathematical, statistical, and perceptual image and video modeling and representation; linear and nonlinear filtering, de-blurring, enhancement, restoration, and reconstruction from degraded, low-resolution or tomographic data; lossless and lossy compression and coding; segmentation, alignment, and recognition; image rendering, visualization, and printing; computational imaging, including ultrasound, tomographic and magnetic resonance imaging; and image and video analysis, synthesis, storage, search and retrieval.
用于图像、视频和多维信号的形成、捕获、处理、通信、分析和显示的理论、算法和体系结构。感兴趣的主题包括：数学，统计，和感知图像和视频建模和表示；线性和非线性滤波、去模糊、增强、恢复和重建退化、低分辨率或层析数据；无损和有损压缩编码；分割、对齐和识别；图像渲染、可视化和打印；计算成像，包括超声、断层和磁共振成像；以及图像和视频的分析、合成、存储、搜索和检索。
--
一级分类：Electrical Engineering and Systems Science        电气工程与系统科学
二级分类：Signal Processing        信号处理
分类描述：Theory, algorithms, performance analysis and applications of signal and data analysis, including physical modeling, processing, detection and parameter estimation, learning, mining, retrieval, and information extraction. The term "signal" includes speech, audio, sonar, radar, geophysical, physiological, (bio-) medical, image, video, and multimodal natural and man-made signals, including communication signals and data. Topics of interest include: statistical signal processing, spectral estimation and system identification; filter design, adaptive filtering / stochastic learning; (compressive) sampling, sensing, and transform-domain methods including fast algorithms; signal processing for machine learning and machine learning for signal processing applications; in-network and graph signal processing; convex and nonconvex optimization methods for signal processing applications; radar, sonar, and sensor array beamforming and direction finding; communications signal processing; low power, multi-core and system-on-chip signal processing; sensing, communication, analysis and optimization for cyber-physical systems such as power grids and the Internet of Things.
信号和数据分析的理论、算法、性能分析和应用，包括物理建模、处理、检测和参数估计、学习、挖掘、检索和信息提取。“信号”一词包括语音、音频、声纳、雷达、地球物理、生理、（生物）医学、图像、视频和多模态自然和人为信号，包括通信信号和数据。感兴趣的主题包括：统计信号处理、谱估计和系统辨识；滤波器设计；自适应滤波/随机学习；（压缩）采样、传感和变换域方法，包括快速算法；用于机器学习的信号处理和用于信号处理应用的机器学习；网络与图形信号处理；信号处理中的凸和非凸优化方法；雷达、声纳和传感器阵列波束形成和测向；通信信号处理；低功耗、多核、片上系统信号处理；信息物理系统的传感、通信、分析和优化，如电网和物联网。
--
一级分类：Physics        物理学
二级分类：Data Analysis, Statistics and Probability        数据分析、统计与概率
分类描述：Methods, software and hardware for physics data analysis: data processing and storage; measurement methodology; statistical and mathematical aspects such as parametrization and uncertainties.
物理数据分析的方法、软硬件：数据处理与存储；测量方法；统计和数学方面，如参数化和不确定性。
--

---
英文摘要：
  Complex demodulation of evolutionary spectra is formulated as a two-dimensional kernel smoother in the time-frequency domain. In the first stage, a tapered Fourier transform, $y_{nu}(f,t)$, is calculated. Second, the log-spectral estimate, $\hat{\theta}_{\nu}(f,t) \equiv \ln(|y_{nu}(f,t)|^2$, is smoothed. As the characteristic widths of the kernel smoother increase, the bias from temporal and frequency averaging increases while the variance decreases. The demodulation parameters, such as the order, length, and bandwidth of spectral taper and the kernel smoother, are determined by minimizing the expected error. For well-resolved evolutionary spectra, the optimal taper length is a small fraction of the optimal kernel half-width. The optimal frequency bandwidth, $w$, for the spectral window scales as $w^2 \approx \lambda_F/ \tau $, where $\tau$ is the characteristic time, and $\lambda_F$ is the characteristic frequency scale-length. In contrast, the optimal half-widths for the second stage kernel smoother scales as $h \approx 1/(\tau \lambda_F)^{1 \over ( p+2) }$, where $p$ is the order of the kernel smoother. The ratio of the optimal frequency half-width to the optimal time half-width satisfies $h_F / h_T ~ (|\partial_t ^p \theta | / |\partial_f^p \theta|)$. Since the expected loss depends on the unknown evolutionary spectra, we initially estimate $|\partial_t^p \theta|^2$ and $|\partial_f^p \theta|^2$ using a higher order kernel smoothers, and then substitute the estimated derivatives into the expected loss criteria.
---
PDF链接：
https://arxiv.org/pdf/1803.03897