# Inverse dft and dft question

1. Oct 25, 2011

### seamie456

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

2. Oct 27, 2011

### jasonRF

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