Hi, how to calculate 3 point fft?

[W_Heisenberg]

Given [1 4 7], looking for its 3 point fft

how to draw the butterfly?

 

[Mityan]

There are no fast algorithms for this. Just DFT. Multiply this vector with 3x3 matrix of fourier coeffs. And sum. Refer to literature for further info.

 

[albert22]

Matlab comand dftmtx(N) (in this case N=3) gives the fourier matrix W. Then multiply as Mityan said X=W x. Where x is your input vector. and X the DFT coefficients vector.

Also with only 3 points you can calculate it even by hand. Using the analysis equations (for N=3):
Re X(k)= sum x cos(2 pi k i / N) for i=0 to N-1
Im X(k)= sum x sin(2 pi k i / N) for i=0 to N-1

(sorry I dont know how to enter formulas sum is the summation sign).

 

[W_Heisenberg]

In this way, is there any butterfly form?

seems not to me.

There are no fast algorithms for this. Just DFT. Multiply this vector with 3x3 matrix of fourier coeffs. And sum. Refer to literature for further info.