通信工程文献翻译——滤波器是输出端的信号瞬时功率与噪声平均功率的比值最大的线性滤波器。其滤波器的传递函数形式是信号频谱的共轭。

因此匹配滤波器对信号做两种处理：

(1)滤波器的相频特性与信号相频特性共轭，使得输出信号所有频率分量都在输出端同相叠加而形成峰值。

(2)按照信号的幅频特性对输入波形进行加权，以便最有效地接收信号能量而抑制干扰的输出功率。

即当信号与噪声同时进入滤波器时，它使信号成分在某一瞬间出现尖峰值，而噪声成分受到抑制。

匹配滤波器广泛用于雷达、声纳和通信。其作用是：

第一，提高信噪比。毫不夸张地说，任何电子系统都有匹配滤波或近似匹配滤波的环节，目的是提高信噪比。

第二，对于大时间带宽积信号，匹配滤波等效于脉冲压缩。因此可以提高雷达或声纳的距离分辨率和距离测量精度。在扩频通信中，可以实现解扩。

匹配滤波器是一种非常重要的滤波器，广泛应用与通信、雷达等系统中。匹配滤波器的推导数学公式看起来很负责，在通信系统、雷达系统、随机信号处理等很多教科书中都有详细的推导过程。最开始的时候，顺着推导的过程，基本也能推导下来，但对其内在的涵义却无半点认识，可以说完全淹没在公式推导的海洋了。

所谓的匹配滤波器，实际上都是在某个准则下的最优。匹配滤波器对应的最优的准则是输出信噪比（SNR）最大。而且还有一个前提条件是在白噪声背景下。推导很多地方都有，最后的结果就是匹配滤波器的表达式为：

H(f)=S*(f)

也即是说，匹配滤波器的频率响应是输入信号频率响应的共轭。这看起来又很简单，那么如何从物理直观上理解匹配滤波器呢？

一方面，从幅频特性来看，匹配滤波器和输入信号的幅频特性完全一样。这也就是说，在信号越强的频率点，滤波器的放大倍数也越大；在信号越弱的频率点，滤波器的放大倍数也越小。这就是信号处理中的“马太效应”。也就是说，匹配滤波器是让信号尽可能通过，而不管噪声的特性。因为匹配滤波器的一个前提是白噪声，也即是噪声的功率谱是平坦的，在各个频率点都一样。因此，这种情况下，让信号尽可能通过，实际上也隐含着尽量减少......

Filter is the ratio of maximum linear filter instantaneous signal power and the noise average power output. The transfer function of the filter is the form of conjugate signal spectrum.

So the matched filter two kinds of signal processing:

The conjugate phase frequency characteristics, the filter phase frequency characteristic and signal, the output signal of all frequency components in the output phase stack and the formation of the peak.

Two, according to the amplitude frequency characteristics of the input waveform signal output power are weighted, so that the most effectively the received signal power and interference uppression.

When the signal and noise and into the filter, the signal components appear peak in a moment, the noise is suppressed.

The matched filter is widely used in radar, sonar and communication. Its role is to:

(1) to improve the signal-to-noise ratio. It is no exaggeration to say, any electronic system has matched filtering or approximate matching filtering step, the purpose is to improve the signal to noise ratio.

(2) for large time bandwidth product signal, matched filter is equivalent to the pulse compression. It can raise a radar or sonar range resolution and ranging accuracy. In spread spectrum communication, can achieve despreading.

The matched filter is a filter is very important, and widely used in communication, radar system. Derivation of mathematical formula matched filter looks very responsible, has a detailed derivation in the communication system, radar system, random signal processing in many textbooks. In the beginning, the derivation process, basic can also are down, but the intrinsic meaning but without understanding, can be said to be completely submerged in the sea of formula.

The matched filter called, actually is optimal in a criterion of. Matched filter corresponding to the criterion is that the output signal-to-noise ratio (SNR) maximum. But there is a premise condition is in white noise background. There are a lot of places are deduced, the final result is a ......