# Inverse dft and dft question

## Main Question or Discussion Point

How does one edit the input sequence and the results so as to be able to calculate the inverse dft with the dft algorthm?

jasonRF
Gold Member
if you define the DFT by:
$$X_k = \sum_{n=0}^{N-1} x_n e^{-i 2 \pi \frac{k}{N} n} = DFT\left(x\right)_k$$
and it inverse DFT by
$$x_n = \frac{1}{N} \sum_{k=0}^{N-1} X_k e^{+i 2 \pi \frac{k}{N} n} = IDFT\left(X\right)_n,$$
then the way to get $x_n$ from $X_k$ using a DFT would be something like,
$$x_n = \frac{1}{N} \left(\sum_{k=0}^{N-1} X_k^* e^{-i 2 \pi \frac{k}{N} n}\right)^* = \frac{1}{N} \left( DFT \left( X^* \right) \right)_n^*$$.
where the asterix represents conjugation. Does that make sense?

jason