Linsker's multi-layer neural network model is considered,
in particular,
development of an oriented receptive field of a cell on layer $G$
is studied mathematically.
We attempt to
investigate which features in his model are essential
for developing oriented receptive fields.
Here we consider a slightly simplified version of Linsker's model
and analyze its process of synaptic weights modification
by computing the Fourier transform of the weight modification rule.
Through our mathematical analysis,
we obtain the following observations:
(1) a Mexican-hat shape function as the correlation function
extracts the Fourier components of a certain frequency,
(2) the shape of the Fourier cosine component is circular symmetric
while that of the Fourier sine component is bi-modal, and
(3) the arbor function determines either the Fourier sine component
or the Fourier cosine component dominates the other.
These observations are also justified by our computer simulations.
Finally we discuss the role of Linsker's parameters $k_1$ and $k_2$.