Hiệu quả của một lựa chọn các sóng khác nhau để lọc một phần của điện tâm đồ (bằng cách sử dụng xấp xỉ đầu tiên) bị ô nhiễm bởi Gaussian hồng nhiễu (SNR = 20 dB). Từ trên xuống dưới, ban đầu (làm sạch) ECG, ECG ồn ào, (8,4) lọc biorthogonal, rời rạc Meyer lọc, Coiflet lọc, symlet (6,6) lọc, symlet lọc | Wavelet Filtering 145 Figure The effect of a selection of different wavelets for filtering a section of ECG using the first approximation only contaminated by Gaussian pink noise SNR 20 dB . From top to bottom original clean ECG noisy ECG biorthogonal 8 4 filtered discrete Meyer filtered Coiflet filtered symlet 6 6 filtered symlet filtered 4 4 Daubechies 4 4 filtered reverse biorthogonal 3 5 reverse biorthogonal 4 8 Haar filtered and biorthogonal 6 2 filtered. The zero-noise clean ECG is created by averaging 1 228 R-peak aligned 1-second-long segments of the author s ECG. RMS error performance of each filter is listed in Table . to the length of the highpass filter. Therefore Matlab s has four vanishing moments3 with 9 LP and 7 HP coefficients or taps in each of the filters. Figure illustrates the effect of using different mother wavelets to filter a section of clean zero-noise ECG using only the first approximation of each wavelet decomposition. The clean upper ECG is created by averaging 1 228 R-peak aligned 1-second-long segments of the author s ECG. Gaussian pink noise is then added with a signal-to-noise ratio SNR of 20 dB. The root mean square RMS error between the filtered waveform and the original clean ECG for each wavelet is given in Table . Note that the biorthogonal wavelets with J K 8 4 3. If the Fourier transform of the wavelet is J continuously differentiable then the wavelet has J vanishing moments. Type waveinfo bior at the Matlab prompt for more information. Viewing the filters using Ipdecon bpdccon lprecon hprecon wf ilters in Matlab reveals one zero coefficient in each of the LP decomposition and HP reconstruction filters and three zeros in the LP reconstruction and HP decomposition filters. Note that these zeros are simply padded and do not count when calculating the filter size. 146 Linear Filtering Methods Table Signals Displayed in Figure from Top to Bottom with RMS Error Between Clean and Wavelet .
