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  • Derivative Estimates of Noisy Signals in a Dynamic Environme

    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
    71 Frankland Road
    Hopkinton, MA 01748
    Tel. (508) 435-9061 x206
    Fax. (508) 435-8136
    E-mail: msmail5.clancye@tsod.lmig.com
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