If we have DFT coefficients, we can reconstruct the signal by using IDFT transform.

Read more:

http://www.cirvirlab.com/index.php/electric/inverse-fourier-transform-and-inverse-dft.html
and simulate

http://www.cirvirlab.com/simulation/IDFT-Inverse-DFT-calculator-online.php

Read more:

http://www.cirvirlab.com/index.php/electric/inverse-fourier-transform-and-inverse-dft.html

http://www.cirvirlab.com/simulation/IDFT-Inverse-DFT-calculator-online.php