I have a constant digital signal that is 1 for every sample and of length 4. 4 point DFT coefficients are $$[4,0,0,0]^T$$ Obviously. I wonder, if I resample the DTFT such that samples are taken at $$w=[\pi/4, 3\pi/4,5\pi/4,7\pi/4]^T $$ If I take the inverse DFT, can i find the same signal as before? If not, what is the effect of shifting the samples?