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Low frequency Butterworth and optimal Wiener ECG filters

Regular ad hoc filters don’t guarantee optimal signal filtering as there are no criteria that evaluate filter characteristics. Usually, filter parameters are calculated empirically, and the best results do filtering. To avoid such a shortage, there are optimal filters used where some criteria optimize parameters. Optimal filtering’s main idea is to give bigger weight coefficients to signal spectra parts where signal noise has less power, and true signal spectral components have bigger power. Let’s project a simple Butterworth filter used as a comparative filter to optimal Wiener DSP filter.Butterworth filter transfer characteristics: Where N indicates filter Tap number. I will skip the Butterworth filter description as the main idea is constructing an optimal Wiener filter. Butterworth filter characteristics are pretty plain: The main disadvantage of the Butterworth filter is that signal is distorted on filter output. If you want minimal signal distortions it is better to use an optimal Wiener filter. Filter chart looks as follows: As you can see, to make this filter functional wee need additional conditions like a signal model reference. Filter coefficients are calculated using MMSE. Root mean square error. Let’s see how it works. Filter input is an ideal signal plus noise: and filter output…

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