For information on designing the digital matched filter using the graphical user interface,
see 6.6 Ps — Plot Burst Spectra and AFC (page 137).
The design procedure computes two sets of filter coecients
and
such that the
instantaneous quadrature samples at a given bin are:
=
= 0
1
×
,
=
= 0
1
×
where N is the length of the filter. The input samples p
n
are centered on the range bin to
which the (I, Q) pair is assigned. Note that some p
n
may overlap among adjacent bins. That
is, the
filter length may be greater than the bin spacing. The overlap introduces a slight
correlation between successive bins, but the longer length allows a better filter to be
designed.
The sums above for I and Q are computed on RVP900 using a flexible FGPA that can
perform billions of sums of products per second.
Reference Phase
The reference phase for each transmitted pulse is computed using the same two FIR sums,
except that b
n
is substituted for p
n
.
For magnetron systems, the N b
n
samples are centered on the transmitted burst.
For Klystron systems, the N b
n
samples may be obtained from the burst pulse
(recommended) or from the CW COHO. If the Klystron is phase modulated by an external
phase shifter (instead of the IFDR digital transmitter board), the samples should be from the
modulated COHO.
Coecients
The
coecients are computed as:
=
× sin
4
+ 2
1
2
, = 0 ... 1
where f
IF
is the radar intermediate frequency, f
SAMP
is the IFDR sampling frequency, and
l
n
are the
coecients of an N-point symmetric low-pass FIR filter that is matched to the
bandwidth of the transmitted pulse. The multiplication of the l
n
terms by the sin() terms
eectively converts to the low-pass filter to a band-pass filter centered at the radar IF.
The formula for the
coecients is identical except that sin() is replaced with cos().
The phase of the sinusoid terms, and the symmetry of the l
n
terms, has been chosen to
have a valuable overall symmetry property when n is replaced with (N-1)-n, that is, the
sequence is reversed:
1
=
1
× sin
4
+ 2
1
1
2
Chapter 7 – Processing Algorithms
173
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