Page 78 - Introduction to Information Optics

Exercises 63
1.13 A sound spectrograph can display speech signals in the form of a
frequency versus time plot which bears the name of logon (spectrogram).
The analyzer is equipped with a narrow band Av = 45 Hz and a wide
band Av = 300 Hz.
a. Show that it is impossible to resolve the frequency and time informa-
tion simultaneously by using only one of these filters.
b. For a high-pitched voice that varies from 300-400 Hz, show that it is
not possible to resolve the time resolution, although it is possible to
resolve the fine-frequency content.
c. On the other hand, for a low-pitched voice that varies from 20-45 Hz,
show that it is possible to resolve the time resolution but not the
fine-frequency resolution.
1.14 We equip the Szillard's demon with a beam of light to illuminate the
chamber, in which it has only one molecule wandering in the chamber, as
shown in Fig. 1.19. Calculate
a. the net entropy change per cycle of operation,
b. the amount of information required by the demon,
c. the amount of entropy change of the demon, and
d. show that with the intervention of the demon, the system is still
operating within the limit of the second law of thermodynamics.
1.15 A rectangular photosensitive paper may be divided into an M x N array
of information cells. Each cell is capable of resolving K distinct gray
levels. By a certain recording (i.e., encoding) process, we reduce the M x N
to a. P x Q array of cells with P < M and Q < N
a. What is the amount of entropy decrease in reducing the number of
cells?
b. Let an image be recorded on this photosensitive paper. The amount of
information provided by the image is l { bits, which is assumed to be
smaller than the information capacity of the paper. If /,- (i.e., /. < //)

1
.m V
P ; : ;, C

0
sx>
A

Fig. 1.19. Szilard's machine by the intervention of the demon. D, photodetector; L, light beams;
C, transparent cylinder; P, piston; m. molecule.