论文标题
时频分析中的随机连续帧
Randomized Continuous Frames in Time-Frequency Analysis
论文作者
论文摘要
最近，提出了一种用于处理高度冗余连续帧的方法。在本文中，我们介绍并分析了这一新理论的应用。蒙特卡洛方法的计算复杂性取决于所谓的线性体积可离散的连续框架（LVD）。 LVD属性意味着Monte Carlo方法所需的系数空间中的样品数与离散信号的分辨率成正比。我们在本文中表明，连续小波变换（CWT）和本地时间频变形（LTFT）是LVD。 LTFT是基于3D时频空间的时频表示，其时间频率更丰富，而不是经典的时频变换，例如短时间傅立叶变换（STFT）和CWT。我们的分析证明，通过LTFT执行信号处理的渐近复杂性与使用STFT和CWT（基于FFT）的信号处理相同，即使LTFT的系数空间较高。
Recently, a Monte Carlo approach was proposed for processing highly redundant continuous frames. In this paper we present and analyze applications of this new theory. The computational complexity of the Monte Carlo method relies on the continuous frame being so called linear volume discretizable (LVD). The LVD property means that the number of samples in the coefficient space required by the Monte Carlo method is proportional to the resolution of the discrete signal. We show in this paper that the continuous wavelet transform (CWT) and the localizing time-frequency transform (LTFT) are LVD. The LTFT is a time-frequency representation based on a 3D time-frequency space with a richer class of time-frequency atoms than classical time-frequency transforms like the short time Fourier transform (STFT) and the CWT. Our analysis proves that performing signal processing with the LTFT has the same asymptotic complexity as signal processing with the STFT and CWT (based on FFT), even though the coefficient space of the LTFT is higher dimensional.
