  High-Frequency (HF) signals are ubiquitous in the industrial world and are of
great use for monitoring of industrial assets. Most deep learning tools are
designed for inputs of fixed and/or very limited size and many successful
applications of deep learning to the industrial context use as inputs extracted
features, which is a manually and often arduously obtained compact
representation of the original signal. In this paper, we propose a fully
unsupervised deep learning framework that is able to extract a meaningful and
sparse representation of raw HF signals. We embed in our architecture important
properties of the fast discrete wavelet transformation (FDWT) such as (1) the
cascade algorithm, (2) the conjugate quadrature filter property that links
together the wavelet, the scaling and transposed filter functions, and (3) the
coefficient denoising. Using deep learning, we make this architecture fully
learnable: both the wavelet bases and the wavelet coefficient denoising are
learnable. To achieve this objective, we propose a new activation function that
performs a learnable hard-thresholding of the wavelet coefficients. With our
framework, the denoising FDWT becomes a fully learnable unsupervised tool that
does neither require any type of pre- nor post-processing, nor any prior
knowledge on wavelet transform. We demonstrate the benefits of embedding all
these properties on three machine-learning tasks performed on open source sound
datasets. We perform an ablation study of the impact of each property on the
performance of the architecture, achieve results well above baseline and
outperform other state-of-the-art methods.
