7. DFT Invertibility

In this short chapter, we’ll derive the inverse of the Discrete Fourier Transform.

As we’ve seen previously, the DFT maps a time-domain input \(x[n]\) to a frequency domain output \(X[m]\). The inverse DFT reverses this process, mapping the frequency domain input \(X[m]\) to the time-domain output \(x[n]\).