Hi all,

I'm looking for any information someone might have in taking derivatives
of noisy signals when the bandwidth of the signal changes over time. My
application is in electromyography (EMG), in which I am interested in
the first and second derivative of the AMPLITUDE of the EMG. The signal
to be differentiated is quite noisy (the noise is roughly as large as
the signal), so I have been using polynomial smoothing filters.
However, the number of data samples to smooth over depends on the
dynamics of the EMG amplitude (when the EMG amplitude is changing
rapidly, the number of samples to smooth over should be small; when the
EMG amplitude is changing slowly, the number of samples to smooth over
should be large). Slowly and rapidly changing EMG amplitudes can exist
within the same recording, thus choosing the smoothing length once for a
complete recording has given me a less than desirable solution. I
expect similar concerns are applicable to techniques such as spline
smoothing, signal differencing, etc.

Is anyone aware of derivative techniques which might adapt their
smoothing to the local character of the signal? Are there other
approaches to this problem?

Any information would be appreciated.

THANK YOU,

Ted Clancy
Liberty Mutual Research Center for Safety and Health