[Discuss-gnuradio] Resampling in the frequency domain

[Alberto di Bene]

A question for all the DSP gurus lurking here.
Suppose I have the spectrum of a signal, obtained via an FFT, and
I want to isolate a portion of it, bring it to baseband and downsample it.
The first idea that comes to mind is to do it in the time domain, first
multiplying the signal by a complex exponential, then lowpass it,
then decimate it.
Would it be possible to simply translate the spectrum by the needed
amount (thus bringing the wanted portion at baseband) and then resample
it so to have a lower sampling rate when the signal is brought back into
the time domain? It looks doable, but I am sure there are issues to
be taken into account (aliasing? windowing? etc.).
Which are the caveats in doing such a process which looks on paper much
faster than working in the time domain?   Thanks in advance.

Alberto