Page 448 - Introduction to Information Optics

Exercises 43 ^
7.38 Refer to the compact joint-transform correlator of Fig. 7.40. Assume that
a 10-mm- thick LiNbO 3 crystal is used for the joint-transform filter and
that the illuminating wavelength is A — 500 nm. If the object separation
is about 2/i = 10 mm and the focal length of the transform lens is 300 mm,
calculate the maximum allowable width of the object.
7.39 Assume that the distribution of a target signal is Gaussianly distributed
as given by

~
271(7

(a) Evaluate the corresponding wavelet matched filter (WMF).
(b) Evaluate the output correlation distribution, if one uses a x — a y = <j,
and a x — a y = 2a, respectively.
(c) If the input target is embedded with an additive white Gaussian noise
T
A = cr/2, calculate the output signal-to-noise ratios for part (b).
7.40 A set of English letters {BPRFEHL} is to be stored in an 8 x 8 neuron
network.
(a) Construct a Hopfield memory matrix.
(b) Construct an IPA memory matrix.
(c) Show that the Hopfield model becomes unstable, but that the IPA
model can recall the letters with unique certainty.
(d) What is the minimum number of letters in this set that can be stored
using the Hopfield model?
7.41 Estimate the minimum number of patterns that can be stored in an
N x N neuron Hopfield network:
(a) For 8x 8 neurons.
(b) For 64 x 64 neurons.
7.42 (a) Repeat the preceding exercise for the IPA model.
(b) Compare the results with those obtained from the Hopfield model.
7.43 Considering the input-output training set of Fig. 7.68 and using the IPA
model,
(a) Develop a one-level heteroassociation neuron network.
(b) Construct a heteroassociation IWM.
(c) Estimate the number of storage patterns for a 4 x 4 neuron hetero-
association network.
7.44 (a) Develop a computer program using the IPA model for a heteroassoci-
ation neural network.
(b) If the input- output patterns of Arabic numerals (1,2,3) are to be
translated into Roman numerals (I, II, III}, construct a heteroassoci-
ation IWM for 8x 8 neurons.
(c) Construct a heteroassociation IWM to translate (I, II, III} as { 1, 2, 3}.