How is the complexity of applying Short term fourier transform over n samples with a moving window of size m amount to O(nmlogm) I have been trying to understand a publication here where Short time fourier transform is applied over n samples in steps of m samples each (m is the size of the moving window). I understand that the computational complexity of the Short time fourier transform for m samples is mlogm.

The operation also consists of extracting energy from the samples. Since there are m samples in the window, I believe it should be O(m) in the worst case.
So , as per my understanding, the complexity of the whole operation should be 
O(n/m * (mlogm + m)) = O(nm). Since there n/m windows and each window has mlogm for fourier transform and m for signal strength extraction.

But the publication shows the complexity as O(nmlogm). Please help me understanding this.
evidently the author is performing an FFT $n$ times (or, if the window hop is not 1 sample, it would be proportional to $n$) and each FFT costs something proportional to $m \log(m)$).  all this is quite normal.