# Deep Filtering: Signal Extraction and Reconstruction Using Complex Time-Frequency Filters

## TL;DR

This paper introduces a novel deep learning method for signal extraction that estimates complex time-frequency filters, improving reconstruction and separation in noisy and distorted audio mixtures compared to traditional mask-based approaches.

## Contribution

The paper proposes a new deep neural network approach to estimate complex TF filters directly, addressing destructive interference and signal reconstruction challenges in single-channel audio separation.

## Key findings

- Outperforms traditional TF mask methods in speech separation tasks.
- Effectively reconstructs signals with packet-loss and interference.
- Demonstrates robustness across various noise and sound classes.

## Abstract

Signal extraction from a single-channel mixture with additional undesired signals is most commonly performed using time-frequency (TF) masks. Typically, the mask is estimated with a deep neural network (DNN), and element-wise applied to the complex mixture short-time Fourier transform (STFT) representation to perform the extraction. Ideal mask magnitudes are zero for solely undesired signals in a TF bin and undefined for total destructive interference. Usually, masks have an upper bound to provide well-defined DNN outputs at the cost of limited extraction capabilities. We propose to estimate with a DNN a complex TF filter for each mixture TF bin which maps an STFT area in the respective mixture to the desired TF bin to address destructive interference in mixture TF bins. The DNN is optimized by minimizing the error between the extracted and the ground-truth desired signal allowing to learn the TF filters without having to specify ground-truth TF filters. We compare our approach with complex and real-valued TF masks by separating speech from a variety of different sound and noise classes from the Google AudioSet corpus. We also process the mixture STFT with notch-filters and zero whole time-frames, to simulate packet-loss during transmission, to demonstrate the reconstruction capabilities of our approach. The proposed method outperformed the baselines, especially when notch-filters and time-frame zeroing were applied.