  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.
