This work introduces a wavelet neural network to learn a filter-bank specialized to fit non-stationary signals and improve interpretability and performance for digital signal processing. The network uses a wavelet transform as the first layer of a neural network where the convolution is a parameterized function of the complex Morlet wavelet. Experimental results, on both simplified data and atmospheric gravity waves, show the network is quick to converge, generalizes well on noisy data, and outperforms standard network architectures.