System information

From this information, the waveform shown in Figure A-10 can then be generated.
As you can see, the resultant waveform is a far more accurate representation of the
original. However, you can also see that there is still room for improvement.
Note that 40 bits were required to encode the waveform at 4-bit reso-
lution, while 156 bits were needed to send the same waveform using 5-
bit resolution (and also doubling the sampling rate). The point is, there
is a tradeoff: the higher the quality of audio you wish to encode, the
more bits are required to do it, and the more bits you wish to send (in
real time, naturally), the more bandwidth you will need to consume.
Figure A-10. Waveform delineated from five-bit PCM
Nyquist’s Theorem
So how much sampling is enough? That very same question was considered in the 1920s
by an electrical engineer (and AT&T/Bell employee) named Harry Nyquist. Nyquist’s
Theorem states: “When sampling a signal, the sampling frequency must be greater than
twice the bandwidth of the input signal in order to be able to reconstruct the original
perfectly from the sampled version.”
#
In essence, what this means is that to accurately encode an analog signal you have to
sample it twice as often as the total bandwidth you wish to reproduce. Since the
#Nyquist published two papers, “Certain Factors Affecting Telegraph Speed” (1924) and “Certain Topics in
Telegraph Transmission Theory” (1928), in which he postulated what became known as Nyquist’s Theorem.
Proven in 1949 by Claude Shannon (“Communication in the Presence of Noise”), it is also referred to as the
Nyquist-Shannon sampling theorem.
606 | Appendix A: Understanding Telephony