图1.14以频率为例描述了分辨率的概念。

Figure 1.14 illustrates the concept ofresolution, in this case in frequency.

Figure 1.14. 频率上两个正弦波的分辨率，每个正弦波的瑞利频率宽度为100Hz。(a)在500赫兹间隔下分辨率良好。(b)在100赫兹间隔下分辨率良好。©在75Hz间隔下处于可分辨的边缘区域。(d)在50赫兹间隔下不能分辨Resolution of two sinusoidsin frequency, each having a Rayleigh width of 100 Hz. (a) Well resolved at 500Hz spacing. (b) Well resolved at 100 Hz spacing. © Marginally resolved at 75Hz spacing. (d) Unresolved at 50 Hz spacing.

该图的(a)部分显示了初始相位为零的两个单位振幅余弦函数之和的正频谱的一部分，一个频率在1000Hz，另一个频率在1500Hz。

Part (a) of the figure shows a portion ofthe positive frequency spectrum of the sum of two unit amplitude cosinefunctions with zero initial phase, one at 1000 Hz and one at 1500 Hz.

该信号可以表示具有相同回波强度但不同径向速度的两个运动目标的多普勒频谱。

This signal could represent the Dopplerspectrum of two moving targets with the same echo strength but different radialvelocities.

根据观测时间可以得到每个sinc函数的主瓣具有100Hz的瑞利宽度(峰值到第一零点宽度)。

The observation time is such that themainlobe of the sinc function contributed by each has a Rayleigh width (peak tofirst null width) of 100 Hz.

两条垂直虚线标出了两个余弦频率的位置。

The two vertical dotted lines mark the twocosine frequencies.

从图中的频谱可以看出两个截然不同的、分离良好的峰值点。

There are two distinct, well-separatedpeaks in the spectrum.

每个峰值对应的实际频率会受到另一个正弦波旁瓣的轻微扰动。

The actual frequency of each peak isperturbed very slightly from the expected value by the sidelobes of the othersinusoid.

尽管如此，这两个信号仍然被认为是能够很好地分辨的。

Nonetheless, these two signal componentsare considered well resolved.

图中的(b)至(d)重复这种频率测量，但两个频率之间的间隔减少到100、75和50Hz。

Parts (b) through (d) of the figure repeatthis measurement with the frequency spacing reduced to 100, 75, and 50 Hz.

在100赫兹间隔处，两个谱峰仍然能够被很好地分辨，随着频率之间的明显扰动增强，当二者之间的频率间隔下降到低于瑞利宽度的75赫兹，再下降到50赫兹时，它们已经模糊为单个谱峰。

At 100 Hz spacing the two spectral peaksare still well resolved, though with more perturbation of the apparentfrequencies, but as the separation drops below the Rayleigh width to 75 andthen to 50 Hz, they blur into a single spectral peak.

在频率间隔为50赫兹时，它们不再被分辨；频谱测量结果不再显示两个分离的信号。

At 50 Hz, they are no longer resolved; thespectrum measurement does not show two separate signals.

在75赫兹时，它们之间勉强可以分辨，尽管在数据中添加一些噪声会使得这种分辨会变得不稳定。

At 75 Hz they are marginally resolved,although a little noise added to the data would make that a precarious claim.

从以上分析来看，为了清晰地分辨这两个频率，两个频率间隔需要大于或等于频率的瑞利宽度。

It appears that a separation of about theRayleigh width or greater is needed for clear resolution of the twofrequencies.

这个演示还表明，单个孤立目标的特征宽度是系统分辨率的主要决定因素。

This demonstration also suggests that thewidth of the signature of a single isolated target is the major determinant ofthe system’s resolution.

雷达的分辨率又决定了分辨率单元的大小。

The resolution of a radar in turndetermines the size of a resolution cell.

在距离、速度或角度上的分辨率单元是指该维度中对雷达在任何时刻接收回波作出贡献的间隔。

A resolution cell in range, velocity, orangle is the interval in that dimension that contributes to the echo receivedby the radar at any one instant.

——本文译自Mark A. Richards所著的《Fundamentals of Radar Signal Processing（Second edition）》

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