フーリエ変換の定義
$$e^{i2\pi f_n t_a} x(f_n) = \sum_{m=0}^{N-1} x(t_m') e^{-i2\pi nm/N}$$
$$x(t_m') = \frac{1}{N} \sum_{n=0}^{N-1} \left[ e^{i2\pi f_n t_a} x(f_n) \right] e^{i2\pi nm/N}$$
$$t_m' = [t_a, t_a + T]$$
$$t_m' = m\Delta t + t_a,~~ m=0,\cdots, N-1$$
$$f_n = [0, F]$$
$$f_n = n\Delta f,~~ n=0,\cdots, N-1$$
$$x(t+T)=x(t),~~T=1/\Delta f$$
$$x(f+F)=x(f),~~F=1/\Delta t$$
$$\Delta t\Delta f = 1/N = 1/(TF)$$