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Re: Woltring Filter cutt-off-frequency <--> VAL/P-value

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  • Re: Woltring Filter cutt-off-frequency <--> VAL/P-value

    First some background for the Biomch-L subscriber. In the GCVSPL
    software, VAL is the "smoothing parameter" of the spline, which occurs
    as a weighting factor in a cost function which is minimized. This
    produces a compromise between how well the spline fits the measurements
    and its smoothness (for a more detailed explanation, see my notes in

    Woltring describes the relationship between VAL and frequency domain
    filter characteristics in his release notes: This states that
    a smoothing spline is equivalent to a

    "double, phase-symmetric
    Butterworth filter, with transfer function H(w) = [1 +
    where w is the frequency, wo = (p*T)^(-0.5/M) the filter's
    frequency, p the smoothing parameter, T the sampling interval,
    and 2M
    the order of the spline. If T is expressed in seconds, the
    cies are expressed in radians/second."

    The VAL calculations that you cited can be derived from this.

    The equation for the transfer function has the property H(w0)= 0.5.
    This is because it is a double Butterworth filter (applied twice).
    Cut-off frequency is usually defined as the frequency at which
    H=1/sqrt(2), and this is why Tony Reina and I have an extra factor in
    the equation.

    You can easily verify the correctness of your spline smoothing by
    processing a sine wave signal at the cut-off frequency. If it comes out
    as a sine wave with its amplitude reduced by a factor 1.41 (=sqrt(2)),
    you have used the correct VAL. I have done this and it came out as


    Ton van den Bogert

    > -----Original Message-----
    > From: * Biomechanics and Movement Science listserver
    > [mailto:BIOMCH-L@NIC.SURFNET.NL] On Behalf Of Rettig, Oliver
    > Sent: Friday, September 15, 2006 5:30 AM
    > Subject: [BIOMCH-L] Woltring Filter cutt-off-frequency
    > VAL/P-value
    > Dear all,
    > we implement an algorithm for gait event detection.
    > For smoothing and derivating the data we want to use the WOLTRING
    > filter. We have found Tony Reina's Matlab MEX interface for the
    > GCVSPL and SPLDER packages based on Dwight Meglan's C Code on the web
    > address
    > We have the problem to find the correct VAL value for the WOLTRING
    > GCVSPL package.
    > We found three approaches:
    > 1. From dan@indy1.motorlab.nsi.eduSun
    > VAL = sampling_freq/(2*PI*cut_off_freq)**(2*order)
    > 2. from Ton van den Bogert
    > w0factor = (sqrt(2.0)-1)**(0.5/m)
    > val = 1.0/dt*(2*pi*f0/w0factor)**(-2*m)
    > 3. Tony Reina
    > VAL = (EMG-sampling_freqency/1000.0) /
    > pow(2*PI*EMG_CUTOFF_FREQUENCY/1000.0/pow( (sqrt(2.0)-1),0.5/M),2.0*M)
    > (including in EMG example)
    > Our questions are:
    > Do anybody know what is the correct equation for calculating the mode
    > value VAL from given cut-off-frequeny?
    > And why the factor 1000 appears in the equation from Tony Reina?
    > Many thanks
    > Kai Kraft
    > Oliver Rettig

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