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DIGISONDE-4D
SYSTEM MANUAL
VERSION 1.2.11
SECTION 1 - GENERAL SYSTEM DESCRIPTION 1-27
will be in phase as long as that set of “stabilizing” coefficients progress negatively in phase at the same rate as
the signal vector is progressing positively. The Fourier transform coefficients serve this purpose since they are
unity amplitude complex exponentials (or phasors), whose only function is to shift the phase of the signal, r(n),
being analyzed.
1:56. Since the Digisonde
®
sounders have always done this spectral integration digitally, the following
presentation will cover only discrete time (sampled data rather than continuous signal notation) Fourier analy-
sis.
=
−
==
N
n
NT
jnk
enrkRtr
0
2
][)()(
F
where r[n] is the sampled data record of the received signal at one certain range bin, n is the pulse number upon
which the sample r[n] was taken, T is the time period between pulses, N is the number of pulses integrated
(number of samples r[n] taken), and k is the Doppler bin number or frequency index. Since a Doppler spec-
trum is computed for each range sampled, we can think of the Fourier transforms as F
56
[] or F
192
[] where the
subscripts signify with which range bin the resulting Doppler spectra are associated.
1:57. By processing every range bin first by pulse compression then by coherent integration, all echoes from
each range have gained at least 21 dB of processing gain (depending on the length of integration) before any
attempt is made to detect them.
NOTE
Further explanation of Equation 1–19 which can be gathered from any good
reference on the Discrete Fourier Transformation, such as [Openheim &
Schaefer, Prentice Hall, 1975], follows. The total integration time is NT, where
T is the sampling period (in the Digisonde-4D, the time period between
transmitted pulses). The frequency spacing between Doppler lines, i.e., the
Doppler resolution, is 2/NT rads/sec (or 1/NT Hz) and the entire Doppler
spectrum covers 2/T rad/sec (with complex input samples this is /T, but
with real input samples the positive and negative halves of the spectra are
mirror image replicas of each other, so only /T rad/sec are represented).
1:58. What is coherently integrated by the Fourier transformation in the Digisonde-4D (as in any pulse-
Doppler radar) is the time sequence of complex echo amplitudes received at the same range (or height) that is,
at the same time delay after each pulse is transmitted. Figure 1-16 shows data layout with range or time delay
vertically and pulse number (typically 32 to 128 pulses are transmitted) horizontally which hold the received
samples as they are acquired. After each pulse is transmitted, one column is filled from the bottom up at regular
sampling intervals, as the echoes from progressively higher heights are received (33.3 msec/5 km). These col-
umns of samples are referred to as height profiles, which are not to be confused with electron density profiles,
but rather mirror the radar terminology of a “slant range profile” (range becomes height for vertical incidence
sounding) which is simply the time record of echoes resulting from a transmitted pulse. A height profile is
simply a column of numeric samples which may or may not represent any reflected energy (i.e., they may con-
tain only noise).
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