To measure sampled sequeces phase values accurately,the phase spectrum of all-phase FFT(apFFT for short)is deeply studied in this paper,and apFFTs property of phase invariant is strictly proved.

To estimate sinusoidal signal’s frequency,amplitude and original phase precisely under noisy circum-stances,a novel time-shift phase difference correcting spectrum method based on all-phase FFT spectral analysis was proposed.

To study the properties of the phase spectrum of all-phase FFT(apFFT for short) and extend its application fields,this paper presents the phase measurement mechanism based on apFFT from the phase spectrum in polar coordinate,vector analysis,matrix analysis,and simulation,etc.

The whole-phase grade has been used to define orebodies of a weathering-crust-type rare-earth deposit and to calculate its reserves.

FIR filter design based on all-phase amplitude-frequency characteristic compensation;

FIR notch filter design based on double phase-shift combination all-phase method;

With all sorts of 3-D factors in frequency domain and time domain being taken into account,an excellent 3-D filter can be constructed by synthesizing the properties of DFT,all-phase signal processing,spectral analysis etc.

To estimate signal frequency and amplitude exactly under noisy circumstances,the excellent property of all-phase DFT restraining spectral leakage is mathematically proved.