Among the frequency domain methods for harmonic analysis

Hann-windowed interpolation algorithms are widely applied. Some of the implementations have similar structures

with merely different interpolation point numbers. By using the relationship between Hann and Rectangular windows

this paper transforms two known Hann-windowed algorithms into their equivalent un-windowed forms

finds out their common features and develops a generalized un-windowed p-point interpolation algorithm. In the process of derivation

an approximate model for the un-windowed discrete Fourier transform(DFT)values of multi-component signals is established

and then two conditions the algorithm coefficients should satisfy are obtained

while a set of coefficients are designed. When the interpolation point number p is 4 or 5

the proposed method is equivalent to two known Hann-windowed methods. The proposed algorithm requires at least 3 interpolation points

when it has the best frequency domain resolution and no corresponding equivalent Hann-windowed form. By combining with the improved DFT recursive formula

the computation amount of the algorithm is linearly related to the interpolation point number p

so the proposed method can greatly reduce the computation amount and provide real-time estimation. Different performances of the proposed algorithms with 3 to 6 interpolation points are compared in the simulation

and the algorithm is applied to the real-time estimation of the current signal of a three-phase motor in the experiment.