Page 221 - Fundamentals of Radar Signal Processing

response (FIR) digital filter is used for this task in Shaw and Pohligh (1995).
Once the lowpass filtering is completed, the spectrum is nonzero only for ω ∈

(–0. 4 π, +0.4π). The sampling rate is then reduced by a factor of two by
discarding every other output sample. The final result is the desired digital I and
Q signals, sampled at a rate of 1.25β samples per second.
As with Rader’s system, the computational complexity is actually reduced
by taking advantage of the properties of decimation and FIR filters. The

decimation is performed immediately after the A/D conversion by splitting the
data into even- and odd-numbered sample streams. The complex modulation by
n
j , which implies both sign changes and real/imaginary interchanges, then
reduces only to sign changes on every other sample in each channel, and the 16-
point FIR filters are replaced with 8-point FIR filters in each channel without
any reduction in filtering quality.

A significant advantage of this system over Rader’s is that the A/D
converter must operate at only 2.5 times the signal information bandwidth,
rather than four times the bandwidth. This is an important savings at high radar
bandwidths. There are three disadvantages. The first is that the lower IF and
sampling rate require sharper transitions in the digital filter, therefore increasing
the filter order necessary to achieve a given stopband suppression and thus the

computational complexity of the filter. The second is the requirement for an
explicit multiplication by jn. Although this reduces to switching and sign
changes, it nonetheless represents extra processing. Third, the final sampling
rate exceeds the signal Nyquist rate by 25 percent, whereas in Rader’s system it
equaled the Nyquist rate. This increases the computational load by 25 percent
over the minimum necessary throughout the remainder of the digital processing.
This may not be a problem in practice. Sampling rates are usually set somewhat

above Nyquist rates anyway to provide a margin of safety, since real signals are
never perfectly bandlimited.
Two other details merit mention. It may appear that modulating the
sideband to baseband before filtering eliminates the possibility of using the
digital filter to suppress DC bias errors from the analog mixer. However, that
same modulation will move any DC term contributed by the mixer to ω = π/2,

where it can still be removed by the lowpass filter. Finally, in the Rader system
the I and Q signals were derived from the upper sideband of the original
bandpass signal, while in the Shaw and Pohlig system the lower sideband was
used. Because the original signal was real valued, its spectrum was Hermitian,
and consequently the spectra of the complex outputs of the two systems, say
*
Y (ω) and Y (ω), are related according to Y (ω) = Y (–ω) so that y [n] = y [n].
*
1
1
2
2
1
2
Thus the I outputs of the two systems are (ideally) identical, while the Q outputs
differ in sign. Clearly, either system could be modified to use the opposite
sideband.