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CHAPTER 9
Sampling Rate
Conversion
In many practical applications of digital signal processing, one is faced
with the problem of changing the sampling rate of a signal, either increasing
it or decreasing it by some amount. The process of converting a signal
from a given rate to a different rate is called sampling rate conversion.
In turn, systems that employ multiple sampling rates in the processing
of digital signals are called multirate digital signal processing systems. In
this chapter we describe sampling rate conversion and multirate signal
processing in the digital domain.
As an example, consider the system shown in Figure 9.1 in which
an analog signal x a (t) issampled using the sampling rate of F s = 1 T
samples/second. The resulting digital signal x(n) issubsequently filtered
using a lowpass filter (LPF) with a cutoff frequency of ω c .
Thus, the output signal y(n) has all its energy in the band 0 ≤ ω ≤
ω c =2πf c . According to the sampling theorem, such a signal may be represented
by the rate of 2f c /T samples/second instead of its existing rate
of F s =1/T . Note that |f c |≤0.5. However, if f c ≪ 0.5, then 2f c /T ≪ F s .
Hence it would seem more advantageous to lower the sampling frequency
to a value closer to 2f c /T and perform signal processing operations at
this lower rate.
Other applications include the need for an optimal interpolation in
computer tomography and efficient multistage designs of narrowband lowpass
filters.
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