low value to some high value, from a side aimed antenna. Chirp signals serve to raise the transmission power
while maintaining a constant bandwidth [2]. Transmission occurs in the range direction, orthogonal to the
radar's path. In contrast, the term cross range, or azimuth, refers to a direction parallel to the path of the
radar. Data collection was performed using the spotlight mode, which ensures finer resolution over smaller
areas than strip-mapping techniques [3]. As the name suggests, for spotlight mode the radar's antenna is turned
at each look-angle to "spotlight" a specific, single target. The set of returned signals, known as the phase history,
are demodulated and processed to produce an image modeling the electromagnetic reflectivity of the ground.
SAR imaging presents several distinct advantages over optical and infrared techniques, including its immunity
to lighting and weather conditions.
The radar device, after transmission, yields an array of complex terms: the phase history of the scene. However,
as SAR is able only to cover a limited range of the scene's spatial frequency, the resulting inverse Fourier
transform of the data will be incomplete. The resolution of the final image depends on the bandwidth, the extent
of the frequency information attained. Bandwidth could be limited by cost constraints or simply by the complexity
of the radar device.
Let F(_) represent the frequency data of the object from a single observation angle. The frequency
information attained by the SAR can be modeled as:
G(w) = H(w)F(w) (
where
1 iff - 0.5 < f < f,+ 0.5fb;
H ' 0 else
defines the frequency limits, with f c representing the center frequency of the radar and f b representing
the bandwidth.
By duality, multiplication in the frequency domain equates to convolution in the time domain:
g(x) = h (x) * f(x)
where * denotes the convolution operator. It can then be easily shown that
h(x) = F-1[H()](
Thus, limiting the bandwidth of the frequency information is equivalent to filtering the image by a sin function.
Thus, limiting the bandwidth of the frequency information is equivalent to filtering the image by a since function.