Abstract: A single pulse and peak signals are decomposed and reconstructed with four types of wavelet bases in different orders. Results demonstrate that the biorthogonal wavelet is of a best fitting to the signals, and the Coifman wavelet is at the last in the four bases. After truncating the expansion series of the wavelets and the Fourier transform, the reconstruction shows that the wavelet reconstruction got higher precision with less number of non-zero coefficients and the local error distribution compared with the Fast Fourier transform we calculated. Thus the wavelet reconstruction can greatly attenuate "Gibbs phenomenon" and limit the errors in a narrow domain around the singularities of the signals.Besides, we also make expansions for the topography of Tibetan plateau in wavelets and Fourier transform. Its reconstruction with or without truncation shows the similar features as the one-dimensional signal reconstruction above.

Key words: orthogonal wavelet, singular signal, FFT, topography of Tibetan plateau