The main spectrums、singular spectrums and cospectrums of matrices over quaternionic sfield are studied.

By introducing the concept of main value of phase difference spectrum,the relationship between probabilistic distribution functions of phase spectrum or phase difference spectrum and their main values are discussed.

From the definition of DFT,calculation method of amplitude spectrum for digital signal is derived in this paper.

In amplitude spectrum of vibrating signal of bearings,there generally exists much disturbance of uniform distributed noise frequencies,which is difficult to be erased by common filter and has a bad influence on identification of bearing vibrating frequency.

When the adhesive quality in multi-layered structures (steel shell, insulation layer and under lying layer) in airbourne solid rocket motors is inspected through oblique ultrasonic pulse echo in immersion, the amplitude spectrum extrema between echoes are used to get signal characters, in order to eliminate signal overlapping in the time field.