A new method of spectral analysis, using an approach we call the empirical mode decomposition (EMD) and the Hilbert spectrum analysis (HSA), is presented. The EMD method decomposes any data into a finite number of intrinsic mode function (IMF) components with time-variable amplitudes and frequencies. This decomposition is nearly orthogonal and totally adaptive. With the decomposition, a Hilbert, rather than Fourier, transform is applied to each IMF component, which gives each component instantaneous frequency and energy density. This approach is totally new, and it is different from any of the existing methods: it uses differentiation to define the frequency rather than the traditional convolution computation; thus, it gives the instantaneous frequency and energy density. The greatest advantage of the new approach is that it is the only spectral analysis method applicable to nonstationary and nonlinear data. To illustrate the capability of his new method, we have applied it to the earthquake record from station TCU129, at Chi-Chi, Taiwan, collected during the 21 September 1999 earthquake. The same record is also analyzed with Fourier analysis, wavelet transform, and response spectrum analysis. Comparisons among the different analysis methods indicate that the Hilbert spectral analysis gives the most detailed information in a time-frequency-energy presentation. It also emphasizes the potentially damage-causing low-frequency energy in the earthquake signal missed by all the other methods.