Discrete spectrum analysis for amplitude correction of damped free vibration response

As response signal of damped free vibration could be considered as product of the harmonic wave and the unilateral exponential function and the rectangle window, that the peak frequency and phase are the frequency and phase of the harmonic wave signal is proved theoretically in this paper. The variation of sampling frequency, error of frequency, damping, phase, which affect the precision of the amplitude of discrete spectrum of damped free vibration signal, is analyzed. One presents a new method to obtain the recovery coefficient for amplitude of unilateral finite length exponential window, which reconstructs a new signal with the damping, frequency, phase that have been estimated. Using DFT, one can obtain the coefficient. When the error of the estimated frequency is zero, the error of amplitude is minor. Theory and simulation show the variation of sampling frequency, error of frequency, damping, phase affects the precision of amplitude severely, and the effect of the variation of one parameter is influenced by the others.