Neurophysiological signals are often noisy, non-sinusoidal, and consist of transient bursts. Extraction and analysis of oscillatory features (such as waveform shape and cross-frequency coupling) in such datasets remains difficult. This limits our understanding of brain dynamics and its functional importance. Here, we develop Iterated Masking Empirical Mode Decomposition (itEMD), a method designed to decompose noisy and transient single channel data into relevant oscillatory modes in a flexible, fully data-driven way without the need for manual tuning. Based on Empirical Mode Decomposition (EMD), this technique can extract single-cycle waveform dynamics through phase-aligned instantaneous frequency. We test our method by extensive simulations across different noise, sparsity, and non-sinusoidality conditions. We find itEMD significantly improves the separation of data into distinct non-sinusoidal oscillatory components and robustly reproduces waveform shape across a wide range of relevant parameters. We further validate the technique on multi-modal, multi-species electrophysiological data. Our itEMD extracts known rat hippocampal theta waveform asymmetry and identifies subject-specific human occipital alpha without any prior assumptions about the frequencies contained in the signal. Notably, it does so with significantly less mode mixing compared to existing EMD-based methods. By reducing mode mixing and simplifying interpretation of EMD results, itEMD will enable new analyses into functional roles of neural signals in behaviour and disease.