I am a PhD in mathematics. Recently, we made an attempt to compute the eigenvalues of non-normalized discrete sine and cosine transforms. Surprisingly, the issue regarding three particular types, DCT-I, DCT-V, and DST-VIII, is rather complicated. Anyway, my question pertains to finding possible applications.
I mean, what could be the next step in the application when you have the eigenvalues and eigenbasis (an orthogonal basis consisting of eigenvectors) of discrete trigonometric transforms? Any references to previous studies?