A group of research students had tried to use a 2D discrete Fourier Transform to characterize the pattern of repeating protein units on a bacteria surface layer image. Since their spectral graph looked unusually messy and their pattern estimates seemed very wrong, my research professor asked me to take a crack at interpreting and cleaning it. My successful analysis helped the research group complete their paper and publish their findings. This project was a pretty neat application of understanding the mathematical assumptions of a technique to properly isolate and interpret the results.

Read full story (with Python code and math analysis): A Fourier Transform Detective Story