my question is about reducing the complexity of radix-2 FFT when the input vector has a specific structure.
For an input vector of x with N elements, the complexity is given by O(N log2 N).
My input vector y with N elements has the structure of: y = [x1 x2]T
x1 = x2
and x1 and x2 vectors have N/2 elements. Is it possible to reduce the complexity of radix-2 FFT for this y vector? I think it is possible to not use one of the N/2 DFT blocks of the FFT algorithm in this case. Can anyone show me what is the complexity for this vector? Thanks in advance.