1398 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 51, NO. 4, APRIL 2003
Fig. 8. Second-generation hybrid RF digital
N
-channel receiver.
Fig. 9. Second-generation hybrid RF digital
N
-channel transmitter.
the conversion process, a parameter that improves slowly in
response to advances in semiconductor technology.
(4)
(5)
A final comment on ADCs is that the spurious terms gen-
erated by converter nonlinearities often exceed the quantizing
noise levels described by the
6-dB per bit rule. The true per-
formance measure of the ADC is the full bandwidth, full-scale
spurious-free dynamic range (SPDR) [11].
The limited dynamic range available from high-speed
ADCs restricts the range of applications for the architectures
presented in Figs. 5 and 6 to IF center frequencies to the low
to mid–100’s of megahertz. To extend the application range of
digital
-channel receivers and digital -channels transmit-
ters, we often use a hybrid scheme in which the initial complex
down conversion is performed with analog I/Q mixers and the
channelization is performed digitally after the ADC. The first
conversion can be considered a block conversion to baseband
that delivers the frequency band of interest to the DSP arena
for subsequent channelization. The hybrid forms of the digital
-channel receiver and the digital -channel transmitter
are shown in Figs. 8 and 9, respectively. DSP techniques are
applied to the digitized I/Q data to balance the gain and phase
offsets in the analog ADC and DAC. DSP-based I/Q balance
correction is a standard signal conditioning task in high-end, as
well as consumer-based, receivers and transmitters.
Fig. 10. Input spectrum of FDM signal to be channelized.
Fig. 11. Conventional channelizer as a replica of analog prototype: down
converters, baseband filters, and resamplers.
II. DIGITAL DOWN CONVERSION
InSection I, we describedtheprocessofsamplingananalog IF
signalor complexanalogbaseband signal containingthesetof
frequency-division-multiplexed (FDM) channels to be further
processed or channelized by DSP techniques. We consider
the input signal to be composed of many equal-bandwidth
equally spaced FDM channels, as shown in Fig. 10. These many
channels are digitally down converted to baseband, bandwidth
constrained by digital filters, and subjected to a sample rate
reduction commensurate with the bandwidth reduction.
The signal-processing task can be performed as a replica of
the analog prototype solution by a DSP-based set of independent
down-conversion processes, as indicated in Fig. 11. For clarity
of presentation, we describe how digital frequency denoted by
the angle
is derived from analog frequency . This change
of variables is shown in (6)–(8). Equation (6) presents a com-
plex sinusoid of frequency
. We note that frequency is the
time derivative of the time evolving phase angle
and has
units of radians/second. The sampled data sinusoid is obtained
by replacing the time variable “
” with the sampled time vari-
able “
,” as shown in (7). Note that the units of the sample
time variable are samples and seconds/sample, respectively. The
angle formed by the product
and or by the equivalent