Page 358 - Analog and Digital Filter Design

Introduction to Digitcl Filters 35

In this equation, B is the 3dB bandwidth and 61‘ is the width of the skirt
response at the minimum detectable (i.e., noise floor) amplitude.

Over-Sampling
Sampling at a rate that is many times the highest analog signal frequency
is called “over-sampling.’’ Over-sampling reduces distortion and reduces the
demands placed on analog anti-alias filters. However, producing more samples
means that the processor must handle more data, which reduces its ability to
perform other tasks or means that a faster processor may be required.

Decimation
Decimation is sometimes used to reduce the data rate. Decimation is the process
of removing samples from the digitized signal. A decimation rate of ‘/2 will
remove every other sample and thus halve the data rate. Similarly. a decimation
rate of $ will only allow every third sample to pass. The decimation process
is useful where the signal of interest cannot be filtered sufficiently to remove
unwanted signals of a slightly higher frequency. In this case both signals are
sampled at a high rate, and then the digitized signal is decimated to reduce the
sampling rate to one suitable for the wanted signal.

The advantage of decimation can be seen in the following example. Suppose the
wanted signal is speech with a bandwidth of lOkHz, but interfering signals are
present at 15 kHz. A sample rate of 24 kHz will meet the requirements of being
greater than twice the maximum analog signal frequency. It would be possible
to attenuate the 15 kHz interfering signal by, say, 60dB with a really good anaiog
filter, but this is not good enough to meet the specification. The sampling fre-
quency of 24kHz for a IOkHz bandwidth signal would be suitable, but an alias
will occur at 9 kHz because of the mixing process between the sampling process
and the 15 kHz interfering signal.

Once the digitized signal contains an alias, it cannot be removed. This problem
can be resolved by sampling at 48 kHz then decimating at ‘12 rate. The 48 kHz
sampling ensures that there is no alias, decimation then provides the same digital
output for the wanted signal. The signal can then be digitally filtered to remove
the remaining traces of the 15 kHz signal.