Waves and oscillatory phenomena are fundamental to understanding the dynamic processes of the solar atmosphere, from magnetoacoustic waves in sunspot umbrae to Alfvénic turbulence in the corona. This Primer reviews and compares a wide range of tools used across disciplines to analyse such signals — with direct relevance to solar and space physics. With particular emphasis on selecting analysis techniques based on data characteristics and scientific objectives, the Primer helps ensure robust, reproducible, and physically meaningful results. While rooted in the solar physics community, the article also highlights applications in seismology, engineering, and biomedical sciences, underscoring the cross-disciplinary power of wave analysis.
Bernhard’s critical discussions on methodological inconsistencies laid the foundation for this project and have long served as a source of inspiration for research endeavours within our WaLSA team and the broader community. Throughout countless WaLSA discussions, his constructive critiques and thought-provoking insights have continually challenged us to refine our approaches, ensure reproducibility across different computational implementations, and push the boundaries of our field.
In recognition of his invaluable contributions, we felt it was the right moment to dedicate this work to Bernhard Fleck, whose intellectual rigour, critical thinking, and passion for scientific inquiry continue to inspire us. It is an honour to have his expertise reflected in this publication, and we wish Bernhard all the very best in his retirement — with the community now looking forward to building upon the scientific legacy he has helped shape, and many more years of collaboration ahead.
* Published Primer: https://www.nature.com/articles/s43586-025-00392-0
* Free view-only access to the Primer: https://WaLSA.tools/nrmp
* Supplementary Information: https://WaLSA.tools/nrmp-si
* WaLSAtools repository: https://WaLSA.tools
P.S. We’ve also created a short animation to accompany and promote the Primer — feel free to have a look (with sound): https://youtu.be/b_rG7Q8fyMU