Inverse dft and dft question

  • Thread starter seamie456
  • Start date
  • #1
1
0

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?
 

Answers and Replies

  • #2
jasonRF
Science Advisor
Gold Member
1,266
311
if you define the DFT by:
[tex]
X_k = \sum_{n=0}^{N-1} x_n e^{-i 2 \pi \frac{k}{N} n} = DFT\left(x\right)_k
[/tex]
and it inverse DFT by
[tex]
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,
[/tex]
then the way to get [itex]x_n[/itex] from [itex]X_k[/itex] using a DFT would be something like,
[tex]
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^*
[/tex].
where the asterix represents conjugation. Does that make sense?

jason
 

Related Threads on Inverse dft and dft question

  • Last Post
Replies
11
Views
6K
  • Last Post
Replies
1
Views
3K
Replies
1
Views
2K
  • Last Post
Replies
7
Views
2K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
10
Views
2K
  • Last Post
Replies
5
Views
491
  • Last Post
Replies
3
Views
1K
Top