Page 77 - Introduction to Information Optics

62 1. Entropy Information and Optics

1 .8 A memory less continuous channel is perturbed by an additive Gaussian noise
with zero mean and variance equal to N. The output entropy and the noise
entropy can be written as

H(B)
H(B/A)

where b = a + c (i.e., signal plus noises), and of = a^ + a? = S + N.
Calculate the capacity of the channel.
1.9 The input to an ideal low-pass filter is a narrow rectangular pulse signal
as given by

Av
fi i i
1> M <^T*
H(v) = < 2 _
JO, otherwise

a. Determine the output response g(t).
b. Sketch g(t) when At Av < 1, AtAv = 1 and ArAv > 1.
c. If

show how this linear phase low-pass filter affects the answers in part (b).
1.10 Consider an mxn array spatial channel in which we spatially encode a
set of coded images. What would be the spatial channel capacity?
1.11 A complex Gaussian pulse is given by

2
u(t) = Kexp(-/lr ),
where M is a constant and

A = a + ib.

Determine and sketch the ambiguity function, and discuss the result as it
applies to radar detection.
1.12 Given a chirp signal, as given by

u(t) =
calculate and sketch the corresponding Wigner distribution.