圖1.14以頻率為例描述了解析度的概念。

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

Figure 1.14. 頻率上兩個正弦波的解析度，每個正弦波的瑞利頻率寬度為100Hz。(a)在500赫茲間隔下解析度良好。(b)在100赫茲間隔下解析度良好。©在75Hz間隔下處於可分辨的邊緣區域。(d)在50赫茲間隔下不能分辨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.

該圖的(a)部分顯示了初始相位為零的兩個單位振幅餘弦函式之和的正頻譜的一部分，一個頻率在1000Hz，另一個頻率在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.

該訊號可以表示具有相同回波強度但不同徑向速度的兩個運動目標的多普勒頻譜。

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

根據觀測時間可以得到每個sinc函式的主瓣具有100Hz的瑞利寬度(峰值到第一零點寬度)。

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.

兩條垂直虛線標出了兩個餘弦頻率的位置。

The two vertical dotted lines mark the twocosine frequencies.

從圖中的頻譜可以看出兩個截然不同的、分離良好的峰值點。

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

每個峰值對應的實際頻率會受到另一個正弦波旁瓣的輕微擾動。

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

儘管如此，這兩個訊號仍然被認為是能夠很好地分辨的。

Nonetheless, these two signal componentsare considered well resolved.

圖中的(b)至(d)重複這種頻率測量，但兩個頻率之間的間隔減少到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赫茲間隔處，兩個譜峰仍然能夠被很好地分辨，隨著頻率之間的明顯擾動增強，當二者之間的頻率間隔下降到低於瑞利寬度的75赫茲，再下降到50赫茲時，它們已經模糊為單個譜峰。

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.

在頻率間隔為50赫茲時，它們不再被分辨；頻譜測量結果不再顯示兩個分離的訊號。

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

在75赫茲時，它們之間勉強可以分辨，儘管在資料中新增一些噪聲會使得這種分辨會變得不穩定。

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

從以上分析來看，為了清晰地分辨這兩個頻率，兩個頻率間隔需要大於或等於頻率的瑞利寬度。

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

這個演示還表明，單個孤立目標的特徵寬度是系統解析度的主要決定因素。

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

雷達的解析度又決定了解析度單元的大小。

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

在距離、速度或角度上的解析度單元是指該維度中對雷達在任何時刻接收回波作出貢獻的間隔。

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.

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

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