Page 135 - Intro to Space Sciences Spacecraft Applications

Introduction to Space Sciences and Spacecraft Applications
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Coding. The method of assigning a particular bit word to each quantiza-
tion level is called coding. (Coding for security purposes is another sepa-
rate process, the mechanics of which are obviously more complicated than
the simple digitization coding discussed here.) Because the signal in the
figure has been split into eight Q-levels, three bits are required to describe
each level separately. The coding used is the specific order in which the
eight different three-bit words are assigned to each level. For the signal
shown in Figure 59,000 has been assigned to the bottom level and a bina-
ry “one” is added to get the coding for each subsequent level.

Sampling. Quantization values are assigned to a signal often enough to
allow the receiver of the information to reconstruct the original signal
(sort of by simply connecting the dots indicated by the digital informa-
tion). The frequency at which a signal is assigned quantization levels
(sampled) is called the sample period (t,).
It should be obvious that if a signal were sampled too infrequently, not
enough information would be available to reconstruct the original signal.
However, as with quantization, sampling too often may result in too large
a number of bits for the system to be practical. It has been shown that if a
signal is sampled at least twice during each sinusoid, there will be enough
information to reconstruct the signal. In terms of frequencies:

f, = > 2fm,, (5-14)

where fs represents the sampling frequency (sampleshec), and fmax repre-
sents the highest frequency in the range of signals being sampled.
Note that the sample period is simply the inverse of the sampling fre-
quency as shown in equation 5-15.
1
t =- (5 - 15)
fs
Transmission Rate. The transmission rate represents the number of bits
per unit time that a digital system creates. Since a sample of n bits is being
taken every t, seconds, and since f, = 1 / t,, the transmission rate (TR) can
be found from:

n
TR = - = n x f, (bps) (5 - 16)
f,