How Can You Compute the Inverse DFT Using a DFT Algorithm?

[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?

 

[jasonRF]

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

jason