as is well known, the 1D Fast Fourier Transform requires $\mathcal{O}\left(N\log_2N\right)$ computations. And is also known that in the case that the input is real, the Hermitian symmetry can be used and we only need to compute half of the spectrum.
My question is, in the real fast Fourier transform we can claim that the complexity of the algorithm is given by $\mathcal{O}\left(\frac{N}{2}\log_2\left(\frac{N}{2}\right)\right)$?
I'm searching for this answer in some books of Fourier transforms but couldn't find any answer.
Thank you, Tiago