I wonder how effective of a test this would be. Are the algorithmic & implementation details of the Fourier transform that important to imaging science? I would imagine that explaining the properties of the FT, it's connection to imaging modalities, etc would be far more relevant than actually coding a DFT.
How would you weight a naive implementation of the DFT vs the FFT?
Write your own Fourier Transform. [If your FizzBuzz questions involve actually writing/coding the FizzBuzz, I'd not request actually writing it...]