Let us say we have a signal $y(k)$ that is of length $K$. I can compute its PSD, also of length $K$. Let us say that this length was not good for finding peaks, so I computed a PSD that was of length $10 \ K$ instead, by doing a zero-padding in the time-domain. I understand that this is equivalent to interpolating the frequency domain result.
So my question is, at this point, if I resample the actual $10 \ K$ length PSD back to be $K$ samples long, would it give me the same result as if I took a $K$ length PSD to begin with? If not, is there any advantage to doing it this way, or would I just be better off sticking to taking a length $K$ PSD to begin with?