The Fourier series is a decomposition of an arbitrary function into a superposition of sinusoidal functions. Some time back, I asked a question about whether it is possible to decompose functions using other families of functions and indeed, it is.
Today's question is much simpler: What do you call such an expansion and the associated transform? Is there a standard name for "a transform whose counterpart for finite domains decomposes a function into the sum of several other functions"?