  Audio super resolution aims to predict the missing high resolution components
of the low resolution audio signals. While audio in nature is a continuous
signal, current approaches treat it as discrete data (i.e., input is defined on
discrete time domain), and consider the super resolution over a fixed scale
factor (i.e., it is required to train a new neural network to change output
resolution). To obtain a continuous representation of audio and enable super
resolution for arbitrary scale factor, we propose a method of implicit neural
representation, coined Local Implicit representation for Super resolution of
Arbitrary scale (LISA). Our method locally parameterizes a chunk of audio as a
function of continuous time, and represents each chunk with the local latent
codes of neighboring chunks so that the function can extrapolate the signal at
any time coordinate, i.e., infinite resolution. To learn a continuous
representation for audio, we design a self-supervised learning strategy to
practice super resolution tasks up to the original resolution by stochastic
selection. Our numerical evaluation shows that LISA outperforms the previous
fixed-scale methods with a fraction of parameters, but also is capable of
arbitrary scale super resolution even beyond the resolution of training data.
