Lorentzian interpolation and generalized interpolation are known as methods of determining accurately the frequency, the relaxation time, and the amplitude of a time domain damped sinusoid whose frequency spectrum is used for interpolation. However, no interpolation formulas based on the Hamming window have been theoretically derived as yet, with conventional interpolation methods modified experientially for the Hamming-apodized spectrum put into use. Those methods have the problems that limitations in the improvement of the interpolation accuracy do exist and that there are no interpolation formulas for determining the relaxation time and the amplitude. In this paper we derive new interpolation formulas by using the ratios of complex adjacent intensities on the discrete Fourier transform spectrum of an exponentially damped sinusoid which is windowed with the Hamming window. Furthermore, we examine the interpolation accuracy by computer simulation and show that the proposed interpolation formulas can very accurately determine the frequency, the relaxation time, and the amplitude. We also investigate the effects of random noise on the interpolation accuracy, and show that the residual errors after interpolation are inversely proportional to the signal-to-noise ratio.