Calculating spectra by sequential filtering

We expand on the method for calculating spectra of inhomogeneous (or non-stationary) fields by sequential filtering [1]. We show that sequential high-pass filtering significantly improves on the low-pass filtering spectrum and the wavelet spectrum, i.e. it is meaningful under broader scaling conditions. We also demonstrate how structure functions fail to capture spectral peaks. While being a valuable tool in turbulence research, structure functions do not provide a proper scale decomposition.

[1] Sadek, M., & Aluie, H. (2018), "Extracting the spectrum of a flow by spatial filtering." Physical Review Fluids, 3(12), 124610. https://doi.org/10.1103/PhysRevFluids.3.124610

[2] Zhao, D., & Aluie, H. (2025), "Calculating spectra by sequential filtering." Journal of Renewable and Sustainable Energy, 17(1). https://doi.org/10.1063/5.0244909