Digital Signal Processing Reference
In-Depth Information
scanning the externally injected carrier over the frequency band-of-interest and
measuring the integrated signal power in a small band around dc, a fairly ac-
curate image of the esd frequency response can be reconstructed. The cut-off
frequency of the low-pass filter in the baseband section determines the fre-
quency resolution of the scanning window. Figure 6.4 shows the test results
of such a measurement, obtained with a resolution bandwidth of 12 MHz. Re-
mark that the center frequency of the receiver is 6 GHz. The effective aperture
of the receive window has been set to 3 ns, which can be deduced from the
main-lobe bandwidth of 650 MHz. The absolute level of the energy spectral
density (esd) in Figure 6.4 depends on several parameters, such as the exter-
nally injected carrier power, the rms aperture width of the receive window,
the gain settings of the variable gain amplifier and the resolution bandwidth
used during the measurement. Because the absolute peak level is of no further
interest for this discussion, the frequency response has been normalized to the
peak esd at the center frequency of the receiver.
- Sensitivity determined by the receive window -
It is important to recognize that the bandwidth of the main lobe alone
is not a correct measure for the total amount of rf energy that is cap-
tured by the front-end or the sensitivity of the front-end in a particular
frequency band. In contrast to what would be expected, the sensitivity
of the receiver improves with a reduced null-to-null bandwidth of the
main lobe.
Intuitively, this can be understood by realizing that if the duration of
the receive window is increased - which is in fact the only way to re-
duce the bandwidth of the main lobe - the receiver indeed allows more
energy to pass to the signal chain. Mathematically, this finding can be
verified by understanding that the peak magnitude of the esd response
is proportional to the square of the window length, which makes that
the total area (energy) under the main lobe increases more or less lin-
early with an increased duration of the receive window. The reader
should also be fully aware of the fact that the spectral shaping tech-
nique used to determine the frequency response of the receive window
does not apply to wideband input signals. This is because the spectral
footprint of the received signal must be
convoluted (
)
with the fre-
quency response of the receiver. It is an easy mistake to suppose that
the spectrum of the received signal is shaped (multiplied) by the mag-
nitude frequency response of the receiver. Keeping this in mind, it can
be seen that there is nothing suspicious in the magnitude frequency
response of the pulse-based receiver being smaller than the spectral
footprint of the received pulse stream.
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