  Signal denoising is a key preprocessing step for many applications, as the
performance of a learning task is closely related to the quality of the input
data. In this paper, we apply a signal processing based deep neural network
architecture, a learnable extension of the wavelet packet transform. As main
advantages, this model has few parameters, an intuitive initialization and
strong learning capabilities. Moreover, we show that it is possible to easily
modify the parameters of the model after the training step to tailor to
different noise intensities. Two case studies are conducted to compare this
model with the state of the art and commonly used denoising procedures. The
first experiment uses standard signals to study denoising properties of the
algorithms. The second experiment is a real application with the objective to
remove audio background noises. We show that the learnable wavelet packet
transform has the learning capabilities of deep learning methods while
maintaining the robustness of standard signal processing approaches. More
specifically, we demonstrate that our approach maintains excellent denoising
performances on signal classes separate from those used during the training
step. Moreover, the learnable wavelet packet transform was found to be robust
when different noise intensities, noise varieties and artifacts are considered.
