For my project, I needed to detect the primary oscillation frequency in a signal data. As I googled around, it turns out that DCT is the best tool to find this (http://www.mech.pku.edu.cn/robot/teacher/wangjiandong/WangHuangLu_ImprovedDCT_CEP_2013.pdf)
My question is: why would you base the analysis on DCT, and not DFT? What would happen if I were to apply the same analysis but with DFT? I can't accept that DCT is "faster" since for the practice of detecting oscillation, even in real time, both are "fast enough" and so speed and computation complexity should not be a factor into deciding which to pick!