I'm trying to uniquely determine a complex function given pairs of real valued functions derived from it. For example, if you have its real and imaginary parts, or phase and the magnitude, the function is uniquely determined from them. But what if you have the magnitude of the function and the magnitude of its fourier transform? ie, are there two distinct functions for which these two properties are identical? What are some other pairs of real valued functions related to the fourier transform that I might use?