I can't find anything on the Internet regarding its practical applications.
Translation, in general, occurs when a series is multiplied with (or "modulated by") a sinusoid. I write "series" because the translation effect can be applied to both the time domain and the frequency domain.
The main thing to keep in mind here is that when you multiply a time ...
You can use a Sinc (or windowed Sinc) kernel for interpolation between FFT/DFT result bins. Note that near DC and Fs/2, the interpolation needs to be circular.
After shifting a peak up and determining its phase, you can again use Sinc interpolation to figure out how it should be represented in some number of nearby (non-fractional) bins.