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DIGISONDE-4D
SYSTEM MANUAL
VERSION 1.2.11
SECTION 1 - GENERAL SYSTEM DESCRIPTION 1-29
Complex Windowing Function
1:59. With T, the sampling period between subsequent samples of the same coherent process, i.e., the same
hardware parameters) defined by the measurement program, the first element of the Discrete Fourier Transform
(i.e., the amplitude of the DC component) will have a spectral width of 1/NT. This spectral resolution may be
so wide that all Doppler shifts received from the ionosphere fall into this one line. For instance, in the mid-
latitudes it is very rare to see Doppler shifts of more that 3 Hz, yet with a 50 Hz spectrum of 16 lines, the
Doppler resolution is 6.25 Hz, so a 3 Hz Doppler shift would still appear to show “no movement”. For sound-
ing, it would be much more interesting if instead of a DC Doppler line, a +3.25 Hz and a –3.25 Hz line were
produced, such that even very fine Doppler shifts would indicate whether the motion was up or down. The DC
line is a seemingly unalterable characteristic of the FFT method of computing the Discrete Fourier Transform,
yet with a true DFT algorithm the Fourier transform coefficients can be chosen such that, the centre of the
Doppler lines analyzed can be placed wherever the designer desires them to be. What was needed was a –½
Doppler line shift which would be correct for any value of N or T.
1:60. Because the end samples in the sampled time domain function are random, a tapering window had to be
used to control the spurious response of the Doppler spectrum to below –40 dB (to keep the SNR high enough
to not degrade the phase measurement beyond 1°). Therefore a Hanning function, H(n), which is a real func-
tion, was chosen and implemented early in the DPS development. The reader is referred to [Oppenheim and
Schafer, 1975] for the definition and applications of the Hanning function. The solution to achieving the ½
Doppler line shift was to make the Hanning function amplitudes complex with a phase rotation of 180° during
the entire time domain sampling period NT. The new complex Hanning weighting function is applied simply
by performing complex rather than real multiplications. This implements a single-sideband frequency conver-
sion of ½ Doppler line before the FFT is performed. In the following equation, each received multipath signal
has only one spectral component (k = D
i
) such that it can be represented as,
i
exp[j2nD
i
]:
P
r(n) = {
i
exp[–j2(nD
i
)} |H(n)| exp[–j2(n/2NT)]
i=1
P
= |H(n)|
i
exp[–j2(nD
i
+ n/2NT))
i=1
Multiplexing
1:61. When sending the next pulse, it need not be transmitted at the same frequency, or received on the same
antenna with the same polarization. With the Digisonde-4D it is possible to “go off” and measure something
else, then come back later and transmit the same frequency, antenna and polarization combination and fill the
second column of the coherent integration buffer, as long as the data from each coherent measurement is not
intermingled (all samples integrated together must be from the same coherent statistical process). In this way,
several coherent processes can be integrated at the same time. Figure 1-16 shows eight coherent buffers, inde-
pendently collecting the samples for two different polarizations and four antennas. This can be accomplished
by transmitting one pulse for each combination of antenna and polarization while maintaining the same fre-
quency setting (to also integrate a second frequency would require eight more buffers), in which case, each
subsequent column in each array will be filled after each eight pulses are transmitted and received. This multi-
plexing continues until all of the buffers are filled with the desired number of pulse echo records. The DPS can
keep track of 64 separate buffers, and each buffer may contain up to 32 768 complex samples. The term
“pulse” is used generically here. For Complementary Coded waveforms a pulse actually requires two pulses to
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