Linear digital filters are at the core of image reconstruction and processing for many coherent optical imaging techniques, such as digital holography (DH) or optical coherence tomography (OCT). They can also be efficiently implemented using fast Fourier transform (FFT) with appropriate transfer/filter functions that operate in the frequency domain. However, even with optimal filter design, they suffer from side effects such as sidelobe generation or resolution limitations, e.g., when using windowing for apodization. Here, we propose a novel, to the best of our knowledge, nonlinear (NL) filter and apply it to coherent (complex-valued) data. The NL filter preserves correct phase information, reduces sidelobes, and can be implemented indirectly by linear filters, making it almost as performant as linear filters. We demonstrate the usefulness of these filters in OCT data processing, showing the separation of background from signal, and an alternative to classical windowing that retains the full width at half maximum (FWHM) resolution of a rectangular window function, but with sidelobe suppression comparable to other window functions. Contrary to many alternatives, it even performs well in proximity to scattering structures that are subject to speckle noise. Because of its simplicity and advantages, we expect to see widespread applications of the technique beyond the demonstrated applications.