----- Original Message -----
From: captbrian <[email protected]>
To: <[email protected]>
Sent: Wednesday, August 25, 2004 8:47 PM
Subject: LF: Re: RE: Key Clicks
Do I assume that "Gaussian" is being used loosely here to indicate a
slope increase at first and a gradual slope decrease at the end of the
followed by a similar shape on the decline. ? I cannot think why there
should be a connection between a curve of statistical random distribution
and a modulation curve for least harmonic production...
Dear Bryan, LF group,
It has that effect - if you could make a truly Gaussian filter, you would
find that the shape of the amplitude vs. frequency response was the same
shape as the normal distribution curve of statistics. You would also find
that the impulse reponse (the output waveform when the input signal is an
infinitesimally short pulse) was the same shape. But if the sole purpose
were to reduce the bandwidth of the unwanted sidebands, it would be better
to use a type of filter with a sharper cut-off, such as a Butterworth or
Chebyshev, since the Gaussian frequency response rolls off quite slowly.
However, the thing which makes a Gaussian filter response really desirable
for many applications in electronics is that it has constant "group delay".
This means that all the frequency components of the signal are delayed by
the same amount as they pass through the filter; in other types of filter,
the group delay varies depending on the frequency (it usually rises rapidly
near the cut-off frequency). Varying group delay means that the different
frequency components making up the signal become "smeared out", arriving at
the output at slightly different times. If you are listening to the filter
output, this is one way in which "ringing" is manifested in filters. For
digital modulation, the result is inter-symbol interference, while
distortion results for phase or frequency modulated signals.
So the point of a Gaussian key-click filter is that it filters the signal
while resulting in the minimum distortion of the waveform - converting the
rectangular pulses into smoothly rounded ones, whilst preserving their
width. Unfortunately, it is not possible to make a filter that has a truly
Gaussian response, but good approximations are possible with Bessel and
Linear phase types.
Cheers, Jim Moritz
73 de M0BMU