Digital Signal Processing Reference
In-Depth Information
used at much higher frequency to output the signal at the carrier
frequency.
For example, using a 0.25 roll off filter for a 1 MSPS modulator,
the baseband I and Q signals will have a bandwidth of 625 kHz.
Using a carrier frequency of 1 GHz, the transmit signal will
require about 1.25 MHz of spectrum centered at 1 GHz.
Until now the transmission path has been our focus. The
receive path is quite similar. The signal is down converted, or
mixed down to baseband. The demodulation process starts with
baseband I and Q signals. The receiver is more complex, as it
must deal with several additional issues. There may be nearby
signals which can interfere with the demodulation process, which
must be filtered out, usually with a combination of analog and
digital filters. The final stage of digital filtering is often the same
pulse shaping filter used in the transmitter
called a matched
filter. The idea is that the same filter that was used to create the
signal is also used to filter the spectrum prior to sampling,
maximizing the amount of signal energy used in the detection (or
sampling process). Because we are using the same filter in the
transmitter and the receiver, the raised cosine filter is usually
modified to a square-root raised-cosine filter. The frequency
response of the raised cosine filter is modified to be the square
root of the amplitude across the passband. This also modifies the
impulse response as well. This is shown in the figures below, for
the same roll off factors.
e
A
B
C
D
Figure 17.11. Square root raised
cosine frequency response.
