THE SCALE REPRESENTATION
THE SCALE REPRESENTATION
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DOI：
10.1109/78.258073
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发表时间：
1993-12-01
影响因子：
5.4
通讯作者：
COHEN, L
中科院分区：
文献类型：
--
作者：
COHEN, L
我们认为“尺度”是一种信号的物理属性，并发展了它的性质。我们提出了一种表示尺度的算子，并研究了它的性质和表示。这允许定义标度变换和能量标度密度谱，该能量标度密度谱指示信号中标度值的强度。我们得到了平均尺度、尺度带宽、瞬时尺度和尺度群延迟的显式表达式。此外，我们还得到了平均时间、平均频率、持续时间、频带宽度等关于尺度变量的表达式。定义了短时变换，并将其用于获得给定时间尺度的条件值。我们证明了当窗口变窄时，可以得到瞬时尺度。给出了尺度的卷积和相关定理。设计了一种用于研究线性标度不变系统的公式。我们推导出时间-尺度和频率-尺度的联合表示，使用与时间-频率情况相同的方法来给出每一个的一般类。作为特例，恢复了Marinovich-Altes和Bertrand-Bertrand的联合分布。给出了时间-频率-尺度三个量的联合表示。给出了局部尺度自相关函数的一般表达式。推导了尺度与时间、尺度与频率的不确定原理。
We consider ''scale'' a physical attribute of a signal and develop its properties. We present an operator which represents scale and Study its characteristics and representation. This allows one to define the scale transform and the energy Scale density spectrum which is an indication of the intensity of scale values in a signal. We obtain explicit expressions for the mean scale, scale bandwidth, instantaneous scale, and Scale group delay. Furthermore, we derive expressions for mean time, mean frequency, duration, frequency bandwidth in terms of the scale variable. The short-time transform is defined and used to obtain the conditional value of scale for a given time. We show that as the windows narrows one obtains instantaneous scale. Convolution and correlation theorems for scale are derived. A formulation is devised for studying linear scale-invariant systems. We derive joint representations of time-scale and frequency-scale, General classes for each are presented using the same methodology as for the time-frequency case. As special cases the joint distributions of Marinovich-Altes and Bertrand-Bertrand are recovered. Also, joint representations of the three quantities, time-frequency-scale are devised. A general expression for the local scale autocorrelation function is given. Uncertainty principles for scale and time and scale and frequency are derived.