We study the expressive power of deep ReLU neural networks for approximating
functions in dilated shift-invariant spaces, which are widely used in signal
processing, image processing, communications and so on. Approximation error
bounds are estimated with respect to the width and depth of neural networks.
The network construction is based on the bit extraction and data-fitting
capacity of deep neural networks. As applications of our main results, the
approximation rates of classical function spaces such as Sobolev spaces and
Besov spaces are obtained. We also give lower bounds of the Lp(1β€pβ€β) approximation error for Sobolev spaces, which show that our
construction of neural network is asymptotically optimal up to a logarithmic
factor