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This is readily seen for an FIR filter, \(\displaystyle In order for a digital filter to have linear phase, its impulse response must have conjugate-even or conjugate-odd symmetry about its midpoint. Notice that the filtered signal (shown in red) has attenuated, broadened and added oscillations around the ECG peak, which is undesirable.įigure 1: IIR lowpass filtering result with phase distortion

The following plot shows the filtering performance of a Chebyshev type I lowpass IIR on ECG data – input waveform (shown in blue) shifted by 10 samples (\(\small \Delta=10\)) to approximately compensate for the filter’s group delay. Yet another application area that requires this, is ECG biomedical waveform analysis, as any artefacts introduced by the filter may be misinterpreted as heart anomalies. This characteristic is essential for audio applications as the signal shape is paramount for maintaining high fidelity in the filtered audio. This preservation of phase means that the filtered signal retains the shape of the original input signal.

they preserve the input signal’s phase relationships. Why do we need linear phase filters?ĭigital filters with linear phase have the advantage of delaying all frequency components by the same amount, i.e. This article discusses the characteristics needed for a digital filter to have linear phase, and how an IIR filter’s passband phase can be modified in order to achieve linear phase using all-pass equalisation filters. This is certainly not true for IIR filters that usually have a highly non-linear phase response, especially around the filter’s cut-off frequencies.