Pulse compression

Pulse compression is a signal processing technique commonly used by radar, sonar and echography to increase the range resolution as well as the signal to noise ratio. This is achieved by modulating the transmitted pulse and then correlating the received signal with the transmitted pulse.

The simplest signal a pulse radar can transmit is a sinusoidal-amplitude pulse, ${\displaystyle A}$ and carrier frequency, ${\displaystyle f_{0}}$, truncated by a rectangular function of width, ${\displaystyle \scriptstyle T}$. The pulse is transmitted periodically, but that is not the main topic of this article; we will consider only a single pulse, ${\displaystyle s}$. If we assume the pulse to start at time ${\displaystyle t\,=\,0}$, the signal can be written the following way, using the complex notation:

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