What are the packages out there for decomposing a signal into a basis of functions? Fourier basis, Radial basis, Cosine basis, …

I need to decompose a signal into a set of basis functions and coefficients, manipulate these coefficients, and reconstruct a *new* signal with the same basis. I found BasisFunctionExpansions.jl but it currently doesn’t export an API to reconstruct a signal given a set of coefficients and a basis.

Interestingly, Python SciPy’s radial basis functions doesn’t seem to have this feature either.