Frequency Estimation Using Complex-Valued Shifted Window Transformer

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 (SR), 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 and the 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, deeming them more suitable for edge and mobile applications. SwinFreq achieves an average improvement of 0.03 in structural similarity index measure (SSIM) over cResFreq and a 5% gain in probability of resolution for closely spaced frequency components. 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 SR 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.