Computing discrete Fourier transform of {1 0} by hand for N=2

[kakolukia786]

Hi, I am learning Fourier transformation by my own. I am reading a book "Fourier Transformation" by R. Bracewell. In chapter 11, in examples of discrete Fourier transforms, it gives for N =2, {1 0} transforms to 1/2{1 1}. I can do this in MATLAB but I can't figure it out how to do it by hand. Searching over the internet, I came across some material but it did not help. Can someone explain me how to get those transforms. Thanks

 

[DrClaude]

Have you looked at http://en.wikipedia.org/wiki/Discrete_Fourier_transform#Definition?

 

[marcusl]

Bracewell's is an excellent book. The result you quote should be obvious except, perhaps, for the normalization in front which would usually be used for the inverse DFT (the forward DFT would have the factor 1). I don't have this book here but look at his definition of the DFT and check the normalization.

 

[ProfMimi]

Computing a discrete Fourier transform is basically the same as computing the coefficients of a Fourier series (except for the normalization factor). If you are confused by this simple question, then reviewing how to compute Fourier series might help.