## Low frequency Butterworth and optimal Wiener ECG filters

Regular ad hoc filters don’t guarantee optimal signal filtering as there is no any criteria that evaluates filter characteristics. Usually filter parameters are calculated empirically and filtering is done by best results. In order to avoid such shortage there are optimal filters used where parameters are optimized by some criteria. The main idea of optimal filtering is to give bigger weight coefficients to signal spectra parts where signal noise has less power and true signal spectral components has bigger power. Lets project simple Butterworth filter that will be used as comparative filter to optimal Wiener DSP filter. Butterworth filter transfer characteristics: Where N â€“ indicates filter Tap number. I will skip description of butterworth filter for now as main idea is constructing optimal wiener filter. Butterworth filter characteristics are pretty plain: Butterworth characteristics with bandpass of 70Hz Main disadvantage of Butterworth filter is that signal is distorted on filter output. If you want minimal signal distortions it is better to use optimal Wiener filter. Filter chart looks as follows: As you can see to make this filter functional wee need additional conditions like signal model reference. Filter coefficients are calculated using MMSE. root mean square error. Lets…