In this paper, the orthogonality of coefficient matrices of wavelet filters is utilized to derive the energy equation for the relation between time-domain signal and its corresponding wavelet coefficients. Using the energy equation, the relationship between the wavelet coefficient error and the reconstruction error is obtained. The errors considered in this paper include the truncation error and quantization error. This not only helps to control the reconstruction quality but also brings two advantages: (1) It is not necessary to perform inverse transform to obtain the distortion caused by compression using wavelet transform and can thus reduce computation efforts. (2) By using the energy equation, we can search for a threshold value to attain a better compression ratio within the range of a pre-specified percent root-mean-square difference (PRD) value. A compression algorithm with run length encoding is proposed based on the energy equation. In the end, the Matlab software and MIT-BIH database are adopted to perform simulations for verifying the feasibility of our proposed method. The algorithm is also implemented on a DSP chip to examine the practicality and suitability. The required computation time of an ECG segment is less than 0.0786 ,s which is fast enough to process real-time signals. As a result, the proposed algorithm is applicable for implementation on mobile ECG recording devices.
