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If I want to remove the baseline drift in my ECG signal, which digital filter should be used without distortion and shift in my filtered output? What are the necessary things I have to look for the proper type of filters (like Chebyshev, Butterworth filter, etc)?

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The easiest approach would be use a high pass FIR filter, mostly because it has a linear phase shift (constant group delay). Chebyshev, Butterworth are IIR type filters so their phase response is nonlinear (mostly) and may change the output.

Also one can considered using wavelet decomposition to eliminate low frequency component. There is a paper called "Baseline Drift Removal and De-Noisingof the ECG Signal using Wavelet Transform", it can easily be found on google. Using MATLAB or Python one can check this out with low effort.

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