Pulse compression is a

signal processing Signal processing is an electrical engineering subfield that focuses on analyzing, modifying and synthesizing '' signals'', such as sound, images, and scientific measurements. Signal processing techniques are used to optimize transmissions, ...

technique commonly used by

radar Radar is a detection system that uses radio waves to determine the distance ('' ranging''), angle, and radial velocity of objects relative to the site. It can be used to detect aircraft, ships, spacecraft, guided missiles, motor vehicles, w ...

sonar Sonar (sound navigation and ranging or sonic navigation and ranging) is a technique that uses sound propagation (usually underwater, as in submarine navigation) to navigate, measure distances ( ranging), communicate with or detect objects on ...

and echography to increase the range resolution as well as the signal to noise ratio. This is achieved by

modulating In music, modulation is the change from one tonality ( tonic, or tonal center) to another. This may or may not be accompanied by a change in key signature (a key change). Modulations articulate or create the structure or form of many pieces, as ...

the transmitted pulse and then correlating the received signal with the transmitted pulse.

Simple pulse

Signal description

The simplest signal a pulse radar can transmit is a sinusoidal-amplitude pulse,

A

and

carrier frequency In telecommunications, a carrier wave, carrier signal, or just carrier, is a waveform (usually sinusoidal) that is modulated (modified) with an information-bearing signal for the purpose of conveying information. This carrier wave usually has ...

f_0

, truncated by a rectangular function of width,

T

. The pulse is transmitted periodically, but that is not the main topic of this article; we will consider only a single pulse,

s

. If we assume the pulse to start at time

t=0

, the signal can be written the following way, using the complex notation: :

s(t) = \begin
 A e^ &\text \; 0 \leq t < T \\
 0 &\text
\end

Range resolution

Let us determine the range resolution which can be obtained with such a signal. The return signal, written

r(t)

, is an attenuated and time-shifted copy of the o