The purpose of this example is to investigate changes in EKG waveform shape that accompany lowpass filtering and smoothing by various amounts. The moral of this investigation is that there is such a thing as "too much" filtering of a signal, and that significant and undesirable changes can occur in waveform shape (and in consequent visual interpretation) when overzealous amounts of filtering are applied.
Here is a component software example in which one waveform of a 4 second epoch of a V3 precordial EKG lead will be subjected to different amounts of lowpass cutoff filtering and smoothing by a rectangle of differing widths:
The sliders can be used to extract any 1 second subsegment of the EKG trace, and then to subject that segment to lowpass filtering at a specific cutoff frequency, and then also to smoothing by convolution with a rectangle of variable width:
Here is the magnitude of the spectrum of the original signal. During the acquisition process, the signal has been filtered both by the external electronics, which has a 4th order falloff at 30 Hz, and by a sharp Fourier lowpass filter at 50 Hz. Note that most of the spectrum exists below 32 Hz, indicating that most of the signal has indeed passed through the electronics and lowpass filter. This seems to be the case for most EKG waveforms: their bandwidth of interest falls mostly below 30 Hz:
Here is a composite result of varying both the lowpass cutoff and the smoothing width of additional filtration applied to the input signal:
(Click for bigger image)
As is suggested from the spectrum above, significant changes do not appear in the waveform until the lowpass filter cuts into the bulk of the spectrum at the lower frequencies. However, even modest amounts of smoothing can produce significant changes in the waveform. The widest smoothing rectangle used corresponds to a timescale of only 1/8 second (well within the realm of either mechanical or electronic filters), but it produces drastic changes in the waveform.
Compare the shape of the waveform at the upper left of the diagram to that at the lower right. In this case, far too much filtering has been applied, so that the shape of the output is almost completely unrelated to the input. Without knowing how much filtering has been applied to the original signal, interpretation is impossible. This caveat applies to all aspects of the data acquisition and analysis process, and should be considered at all times.
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