  In this work we propose a method for learning wavelet filters directly from
data. We accomplish this by framing the discrete wavelet transform as a
modified convolutional neural network. We introduce an autoencoder wavelet
transform network that is trained using gradient descent. We show that the
model is capable of learning structured wavelet filters from synthetic and real
data. The learned wavelets are shown to be similar to traditional wavelets that
are derived using Fourier methods. Our method is simple to implement and easily
incorporated into neural network architectures. A major advantage to our model
is that we can learn from raw audio data.
