Are you an EPFL student looking for a semester project?
Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.
Concept
Pulse compression
Summary
Pulse compression is a signal processing technique commonly used by radar, sonar and echography to either increase the range resolution when pulse length is constrained or increase the signal to noise ratio when the peak power and the bandwidth (or equivalently range resolution) of the transmitted signal are constrained. This is achieved by modulating the transmitted pulse and then correlating the received signal with the transmitted pulse.
The ideal model for the simplest, and historically first type of signals a pulse radar or sonar can transmit is a truncated sinusoidal pulse (also called a CW --carrier wave-- pulse), of amplitude and carrier frequency, , truncated by a rectangular function of width, . The pulse is transmitted periodically, but that is not the main topic of this article; we will consider only a single pulse, . If we assume the pulse to start at time , the signal can be written the following way, using the complex notation:
Let us determine the range resolution which can be obtained with such a signal. The return signal, written , is an attenuated and time-shifted copy of the original transmitted signal (in reality, Doppler effect can play a role too, but this is not important here.) There is also noise in the incoming signal, both on the imaginary and the real channel. The noise is assumed to be band-limited, that is to have frequencies only in (this generally holds in reality, where a bandpass filter is generally used as one of the first stages in the reception chain); we write to denote that noise. To detect the incoming signal, a matched filter is commonly used. This method is optimal when a known signal is to be detected among additive noise having a normal distribution.
In other words, the cross-correlation of the received signal with the transmitted signal is computed. This is achieved by convolving the incoming signal with a conjugated and time-reversed version of the transmitted signal. This operation can be done either in software or with hardware. We write for this cross-correlation.
Official source
About this result
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.