Page 129 - DCAP104_EXPOSURE_TO_COMPUTER_DISCPLINES

Exposure to Computer Disciplines

Notes Given a specific bandwidth limitation, the rate at which data can be transferred can be
determined. If the bandwidth is W (in Hz), and the modulation type is M-ary, the rate
at which data can be transferred, given in bits per second (also known as the baud rate),
R, is given by
R = W Log 2M

It would now appear that the free lunch principle (i.e. there is none) has been violated.
Given the same bandwidth, which is determined by the pulse duration, the data rate may
be extended by using a higher M-ary modulation type. As you may suspect, this will not
succeed indefinitely. Ultimately, increasing the bit content of each pulse has the effect
of lowering the signal-to-noise ratio. A way to illustrate this is to consider M-ary FSK.
Starting with BFSK, the bandwidth limits the difference between the two frequencies.
If the same interval is further subdivided to make 16-ary FSK, the difference between
any two adjacent frequencies has been reduced by 1/16 making it more difficult to tell
them apart (especially in the presence of noise). This is quantified as a reduction in the
signal-to-noise ratio. This is also true for all other M-ary systems. Continued operation
of a system will low SNR will lead to an increase in the error rate
Probability of Error as SNR

Clearly, the data rate cannot be increased indefinitely without affecting performance. This
result is expressed in the Hartley-Shannon law for the capacity:

C = R Log (1 + S/N)
where:

C = capacity in bits per second (bps)
S/N = signal-to-noise ratio (depends of modulation type and noise).

6.4.1.7 Minimum Shift Keying (MSK)
This is a technique used to find the minimum signal bandwidth for a particular method
(usually FSK). In BFSK, is the two frequencies are not chosen to be far enough apart, then
it will become impossible to discriminate the two levels. The condition for the difference
in frequencies, DfMSK, such that the two levels can be determined accurately is

DfMSK = 1/(4td)
where td is the pulse duration as previously discussed. MSK is considered to be the most
efficient way to use a given bandwidth. It maximizes the reliability (which is related to
S/N) within a given bandwidth.

6.4.2 Analog Data with Digital Signals
A digital signal can be transmitted over a dedicated connection between two or more
users. In order to transmit analog data, it must first be converted into a digital form. This
process is called sampling, or encoding. Sampling involves two steps:
(a) Take measurements at regular sampling intervals, and

(b) Convert the value of the measurement into binary code.

122 LOVELY PROFESSIONAL UNIVERSITY