Based on the Fourier analysis, the estimation errors of frequency char acteristic was given by a mathematical expression, and the estimation error dist ributions of the two and the three dimensional frequency responses were demonstr ated by a simulation method. The results show that the effect of the initial pha se on the estimation error of the frequency characteristic is remarkable. Beside s of the estimation error with periodicity, it has other special properties, suc h as the local extremum, asymmetry contribution, as well as the whole tendency o f distribution, which make the error distribution much more complicated, and res ult in low accuracy of further signal processing, for instance, the parameter re cognition losing estimation accuracy in vibration modal analysis. Therefore, the given investigation result is valuable for signal processing in theory and in e ngineering practice.