The respiratory signal can be accurately evaluated by single-channel electrocardiogram (ECG) processing, as shown in recent literature. Indirect methods to derive the respiratory signal from ECG can benefit from a simultaneous study of both respiratory and cardiac activities. These methods lead to major advantages such as low cost, high efficiency, and continuous noninvasive respiratory monitoring. The aim of this paper is to reconstruct the waveform of the respiratory signal by processing single-channel ECG. To achieve these goals, two techniques of decomposition of the ECG signal into suitable bases of functions are proposed, such as the empirical mode decomposition (EMD) and the wavelet analysis. The results highlight the main differences between them in terms of both theoretical foundations, and performance achieved by applying these algorithms to extract the respiratory waveform shape from single-channel ECG are presented. The results also show that both algorithms are able to reconstruct the respiratory waveform, although the EMD is able to break down the original signal without a preselected basis function, as it is necessary for wavelet decomposition. The EMD outperforms the wavelet approach. Some results on experimental data are presented.