How to find out the center frequency and bandwidth accurately by looking for the spectral lines after fft?

Let the sampling data be X(i), I= 1, 2…N, and n is the number of sampling points.

The power spectrum is S(j), j= 1, 2…M, where m is the number of frequencies (M=N/2) and the frequency value is f(j), then

(1) center frequency: fc = σ (s (j) * f (j))/σ s (j)

⑵ root mean square frequency: sqrt (σ (s (j) * f (j) * f (j))/σ s (j))

⑶ frequency standard deviation: sqrt (σ (s (j) * (f (j)-fc) * (f (j)-fc))/σ s (j))

(4) frequency concentration: (1-(σ ∣ (s (j) * (f (j)-fc)) ∣/σ (f (j) * s (j)) *100%.

5] Maximum peak frequency: the frequency where the maximum power spectrum is located.

σ represents the sum of j= 1~M in the following formula.