Recent advances have made it possible to create deep complex-valued neural networks. Despite this progress, many challenging learning tasks have yet to leverage the power of complex representations. Building on recent advances, we propose a new deep complex-valued method for signal retrieval and extraction in the frequency domain. As a case study, we perform audio source separation in the Fourier domain. Our new method takes advantage of the convolution theorem which states that the Fourier transform of two convolved signals is the elementwise product of their Fourier transforms. Our novel method is based on a complex-valued version of Feature-Wise Linear Modulation (FiLM) and serves as the keystone of our proposed signal extraction method. We also introduce a new and explicit amplitude and phase-aware loss, which is scale and time invariant, taking into account the complex-valued components of the spectrogram. Using the Wall Street Journal Dataset, we compared our phase-aware loss to several others that operate both in the time and frequency domains and demonstrate the effectiveness of our proposed signal extraction method and proposed loss. In this work, we introduced a new complex-valued framework for signal retrieval and signal separation in the Fourier domain. As a case sudy, we considered audio source separation. We proposed a new masking method based on a complex-valued version of the Feature-wise Linear Modulation (FiLM) model, allowing to perform local ensembling and yielding a beneficial regularization effect. We also proposed a new phase-aware loss taking, explicitly, into account the magnitude and phase of the reference and estimated signals. In our study, phase proved to be an important factor that should be taken into account in order to improve the quality of the separation in terms of SDR. The phase-aware loss improves over other frequency and time-domain losses. Our deep separator draws its power from the compelling properties of complex-valued neural networks and the proposed masking method. Our finding might shed light on the deep complex-valued neural networks' tendency to solve challenging tasks where the data lie in the complex space and where it could be represented in the frequency domain. We view these results as an opportunity to pursue a more systematic investigation of the underpinning of complex-valued representation success. We believe that our proposed method could lead to new research directions where signal retrieval is needed. 6 Appendix
New Signal Extraction Method in the Fourier Domain