# Pulse distortion low pass filter and group delay

What is really meant by pulse distortion? I have come across several paragraphs which mentions the cause of the pulse distortion is group delay. But doesn't a LP filter still distort a pulse even though the filter would have a constant group delay? I mean a LP filter attenuates the amplitude of an input differently at different frequencies. A pulse would be composed of superimposed sinusoids at different frequencies and each sine component of the pulse will be attenuated differently by the filter. Wouldn't that cause a distortion as well?

I ask this because the sources I come across never mentions this and relate the distortion only to the group delay. So I suspect maybe I don't know the true definition of pulse distortion. Would you call a pulse distorted if it is filtered by a LP filter with a constant group delay?

I would call a pulse distorted if its shape (value over time) and/or its spectrum (frequency content) has changed between input and output of the filter.

Theoretically an ideal pulse (with infinitely steep slopes) has an infinite spectrum, that means that anything that changes that spectrum will distort the pulse. A filter will change the spectrum so it will distort the pulse.

Even if the filter would have a constant group delay (a constant delay for all frequencies) but the filter would still affect the amplitudes of some frequencies the pulse would distort as the spectrum would be changed.

If the filter would have a constant group delay (a constant delay for all frequencies) and not affect the amplitude of any frequency the pulse would not distort, it would only be delayed (in time).

If your input pulse is not ideal, meaning its slopes are limited in their steepness, then the spectrum of this pulse will not extend into infinitely high frequencies. Instead it will have a limited spectrum.

If the filter only affects (attenuates) the frequencies that are not present in the spectrum of the pulse and the filter has a constant group delay for all frequencies, then the pulse would not be distorted as nothing was changed by the filter.

So: it depends on the pulse and the filter. With an ideal pulse, filtering it will change (distort) the pulse.

A pulse will be distorted yes but, the point is, that if you are only interested in a certain band of frequencies say from DC to 10 kHz and, the filter has (near) constant group delay up to 10 kHz, then frequencies beyond that frequency can be disregarded.

Would you call a pulse distorted if it is filtered by a LP filter with a constant group delay?

In short, no low pass filter (of any order or type) can perfectly pass a pulse because that pulse will have an infinite number of harmonics and, you reach a point where things go pear-shaped.

Bessel Filters are reputed to achieve both a low-pass response and minimal pulse distortion. Subject to certain optimization criteria.

I recall a project where group-delay needed to be flat across some bandpass portion of the incoming spectra, to ensure FM (frequency modulated) signals would retain at least 40dB SignalNoiseRatio. The group-delay requirement was low nanoseconds of delta-time, in 10 or 20MHz filters. These filters were custom designed, inhouse.