WVDNet: Time-Frequency Analysis via Semi-Supervised Learning

The bilinear based method is one of the commonly used tools in time-frequency analysis (TFA) fields. However, it suffers from the trade-off of high resolution and cross-term interference. We propose WVDNet, a semi-supervised learning model for time-frequency analysis based on the Wigner-Ville distribution (WVD), to reduce the cross-term existing in WVD and relax the requirements of the training data set. The proposed WVDNet is based on the Mean-Teacher model to enable the task model to exploit the unlabeled training data. We first build a synthetic data set for model training, that contains different kinds of amplitude-modulated and frequency-modulated (AM-FM) signals. Next, a task model of WVDNet is designed and the consistency regularization based method is utilized to promote model training. Finally, experiments are conducted on both synthetic and real-world data, showing the effectiveness of suppressing cross-term and strong generalization ability.

I. Introduction

Time-frequency analysis (TFA) has been regarded as a promising method for analyzing signals from a joint time-frequency perspective, which has been applied in many scenarios [1], [2]. There are kinds of TFA methods proposed for addressing different issues, mainly including the linear, bilinear, and non-linear TFA methods. The former principally includes short-time Fourier transform [3], continuous wavelet transform [4], S-transform [5], etc. Since the linear TFA methods often adopt a sliding time window to crop the analyzed signal and then transfer the cropped signals to the TF spectrum, whose TF resolution is limited by the Heisenberg Uncertainty principle [4]. Compared to linear TFA methods, the bilinear TFA methods could provide the higher TF resolution. However, the bilinear based methods, which mainly consist of the Wigner-Ville Distribution (WVD) and the Cohen's class based transforms [6], are limited by the unwanted cross-term interferences. The presence of cross-term makes it difficult to analyze signal characteristics accurately. There are also several non-linear based TFA methods, such as sparse TFA methods [7], [8] and matching pursuit [9]. This kind of methods often suffers from the expensive calculation and the difficulty in parameter selection, which limits their wide applications.