Frequency Estimation Using Complex-Valued Shifted Window Transformer

Abstract: Estimating closely spaced frequency components of a signal is a fundamental problem in statistical signal processing. In this letter, we introduce 1-D real-valued and complex-valued shifted window (Swin) transformers, referred to as SwinFreq and CVSwinFreq, respectively, for line-spectra frequency estimation on 1-D complex-valued signals. Whereas 2-D Swin transformer-based models have gained traction for optical image super-resolution, we introduce for the first time a complex-valued Swin module designed to leverage the complex-valued nature of signals for a wide array of applications. The proposed approach overcomes the limitations of the classical algorithms such as the periodogram, MUSIC, and OMP in addition to state-of-the-art deep learning approach cResFreq. SwinFreq and CVSwinFreq boast superior performance at low signal-to-noise ratio SNR and improved resolution capability while requiring fewer model parameters than cResFreq, thus deeming it more suitable for edge and mobile applications. We find that the real-valued Swin-Freq outperforms its complex-valued counterpart CVSwinFreq for several tasks while touting a smaller model size. Finally, we apply the proposed techniques for radar range profile super-resolution using real data. The results from both synthetic and real experimentation validate the numerical and empirical superiority of SwinFreq and CVSwinFreq to the state-of-the-art deep learning-based techniques and traditional frequency estimation algorithms. The code and models are publicly available at https://github.com/josiahwsmith10/spectral-super-resolution-swin.