INVERSION OF SYNTHETIC APERTUR,E R,ADAR (SAR) - MSpace ...

vlrere ø6 is a angular center fi'equeucy, p :2¡rLÍ lT
is tlie FM slope, and ,4
is a constant amplitude. Figule 3.3 shows a tlansmittecl rectangular waveforrn
of a linear FM pulse chalactelized by the lorver frequency cornponents
at the beginning and the highel fi'equency cornponents at tlie encl of the
pulse. The retuln echo at the leceiver will l¡e sir¡ilal to tlie transmittecl
signal in tirne-frequency chalactelistics as shorvn in Figure 3.a (a) and (b).
If the receiver acts, as shown in Figure 3.4 (c), to delay tlie lower frequency
components more than tlie higher frequency cornponents at the eucl of the
pulse, this is a tinie cornpression of the pulse as shown in Figule 3.4 (d).
This time delay filter is charactelizecl by the invelse tine-frecluelcy slope
irr conrparison with that of the transmitted pulse, and is called a møtched
fiIter. The chalacteristics of a rnatchecl filter are (Cook and Bernfelcl 1967):
1) If the signal spectrum is desclibed by s(ø), then the fiequency response
function H (a,) of a filter that results il a maximurr signal-to-noise ratio
for the filter output is the complex conjugate of the spectlum function,
or' f/(cu) x s (c,.,
)- .
2) If the signal waveform is clefined by s(f), impulse response of the filter'
meeting the condition of 1) is the tirne invelse of the signal s(t), that
is å(t) c< s(-l).
Thus the irnpulse Lespoìse of the flltel matched to the signal in Eq.(3.15) is
nut : \F,e,t
: ,P
*"("*-#)
T
-t