For example, if my histogram has N bins from x_min to x_max, so the width of one bin is equal to N / (x_max - x_min). The output histogram after FFT is same size N, but what about x_limits? As I understand, it should be from -1 / [N / (x_max - x_min)] to 1 / [N / (x_max - x_min)], right?

Oh, yes, of course: binâ€™s width is W = (x_max - x_min) / N. I mean, I guessed that x limits is from (-1 / W) to (1 / W). Thanks.
Hope, someone helps.