Digital Signal Processing Reference
In-Depth Information
The high-frequency content of these plotted I and Q signals
can cause problems, because in most systems it is important to
minimize the frequency content, or bandwidth, of the signal. We
have already discussed frequency response, where a low-pass
filter removes fast transitions or changes in a signal (or eliminates
the high-frequency components of that signal). If the frequency
response of the signal is reduced, this is the same as reducing its
bandwidth. The smaller the bandwidth of the signal, the more
signal channels and therefore capacity can be packed into a given
amount of frequency spectrum. Thus the channel bandwidth is
often carefully controlled.
A simple example is FM radio. Each station, or channel, is
located 200 kHz from its neighbor. That means that each station
has 200 kHz spectrum, or frequency response, it can occupy. The
station on 101.5 is transmitting with a center frequency of
101.5 MHz. The channels on either side transmit with center
frequencies of 101.3 and 101.7 MHz. Therefore it is important to
restrict the bandwidth of each FM station to within
100 kHz,
to ensures it does not overlap or interfere with neighboring
stations. The bandwidth is restricted using a low-pass filter. Video
channels are usually several MHz bandwidth, but the same
concept applies.
The signal's frequency response, or spectrum, can be shifted
up or down the frequency axis at will, using a complex mixer, or
multiplier. This is called up- or downconversion.
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17.3 Pulse Shaping Filter
To accomplish frequency limiting of the modulated signal, the
I and Q signals are low-pass filtered. This filter is often called
a pulse shaping filter, and it determines the bandwidth of the
modulated signal. The filter time domain response is also
important. Assuming an ideal low-pass filter is used where
symbols are generated at a rate (R) of 1 MSPS. The period T is the
symbol duration, and equal to 1 in this example. The relationship
between the rate R and symbol period T is:
R
¼
1 / T and T
¼
1/R
Alternating with positive and negative I and Q values at each
sample interval (this is the worst case in terms of high frequency
content), the rate of change will be 500 kHz. So we would start
with a low-pass filter with passband of 500 kHz.
This filter will have the sin(x) / x or sinc impulse response. The
impulse response is centered in Figure 17-6, along with preceding
and following symbol responses. It has zero crossings at intervals
