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> Dear All
> I am a postgrad student looking at quantifying postural stability during
> quiet standing. Using a force plate to analyse mechanical displacement as
> a function of time provides an electrical signal (normally a voltage, V)
> which is a direct analogue of the displacement of the subject. After
> amplification, this voltage is sampled at regular time intervals to
> provide the primary time-domain signal of V as a function of t.
>
> In the frequency domain, Centre of Pressure (COP) summary measures have
> previously been reported using Mean Power Frequency (MPF) measurements
> (Carpenter, Frank et al. 2001,Gait & Posture 13:1: 35-40) (Hasan, Robin et
> al. 1996, Gait and Posture 4:11-20). I am familiar with two calculations
> for Mean Power Frequency, MPF (electrical) and MPF (mechanical). I would
> be keen to hear of peoples opinion as to which calculation is most
> appropriate method to use when evaluating static balance test calculating
> COP excursions in the frequency domain.
>
> In case you are not immediately familiar with MPF, below are two different
> calculations (apologies for the length!).
>
> Many thanks in advance.
> Liz Bryant
> School of Health Professions, University of Brighton, UK
> tel: (44) 1273 643945
> fax: (44) 1273 643944
> email: E.Bryant@bton.ac.uk
>
>
>
> MPF is a weighted average frequency in which each frequency component, f,
> is weighted by its power, P. (eg. P1 is the power of f1). Thus
>
> Equation 1
> MPF = (f1*P1+f2*P2+ ... + fn*Pn) / (P1 + P2 + ... + Pn)
>
> ie. the MPF is obtained by summing the (frequency times power) of the
> components and dividing by the sum of the powers. This is a straight
> forward parameter but a potential confusion arises from the definition of
> the power used in the Equation 1.
>
> In normal use, P is taken to be proportional to (V*V)max. This definition
> is based on the electrical origin of this type of analysis, since power in
> an (alternating) electrical signal is proportional to (V*V)max (and the
> resistence which is the same for each component and so may be ignored).
>
> So the power P1 at frequency f1 is proportional to (V*V)max,1 or more
> generally the power Pi is proportional to (V*V)max,i. Hence this
> "electrical" MPF is evaluated from:
>
> Equation 2
> MPF (electrical) = (f1*[V*V]max,1 + f2*[V*V]max,2 + ... + fn*[V*V]max,n) /
> ([V*V]max,1 + [V*V]max,2 + ... + [V*V]max,n)
>
> However, as stressed above, the voltage signal, V (t) is an electrical
> analogue of the original mechanical motion, x (t). The DFT spectrum of
> the mechanical time-domain signal would comprise a graph of the vibration
> amplitude, A, against frequency f for each of the mechanical oscillation
> components. Eg. A1 is amplitude at frequency f1 or more generally Ai is
> amplitude at frequency fi.
>
> Equation 3
> x = A sin (2*pi*f*t)
>
> The power required to maintain the oscillation given by Equation 3 is
> proportional to (Ai*fi)^2 and the electrical analogue of this is
> (fi*Vmax,i)^2. Therefore if the MPF of the mechanical motion is required,
> it should be evaluated from:
>
> Equation 4
> MPF (mechanical) = (f1*[f1*Vmax,1]^2 + f2*[f2*Vmax,2]^2 + ... +
> fn*[fn*Vmax,n]^2) / ([f1*Vmax,1]^2 + [f2*Vmax,2]^2 + ... + [fn*Vmax,n]^2)
>
> Equation 4 will, in general, give a different value for MPF from Equation
> 2.
>
>
>
>
>
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> I am a postgrad student looking at quantifying postural stability during
> quiet standing. Using a force plate to analyse mechanical displacement as
> a function of time provides an electrical signal (normally a voltage, V)
> which is a direct analogue of the displacement of the subject. After
> amplification, this voltage is sampled at regular time intervals to
> provide the primary time-domain signal of V as a function of t.
>
> In the frequency domain, Centre of Pressure (COP) summary measures have
> previously been reported using Mean Power Frequency (MPF) measurements
> (Carpenter, Frank et al. 2001,Gait & Posture 13:1: 35-40) (Hasan, Robin et
> al. 1996, Gait and Posture 4:11-20). I am familiar with two calculations
> for Mean Power Frequency, MPF (electrical) and MPF (mechanical). I would
> be keen to hear of peoples opinion as to which calculation is most
> appropriate method to use when evaluating static balance test calculating
> COP excursions in the frequency domain.
>
> In case you are not immediately familiar with MPF, below are two different
> calculations (apologies for the length!).
>
> Many thanks in advance.
> Liz Bryant
> School of Health Professions, University of Brighton, UK
> tel: (44) 1273 643945
> fax: (44) 1273 643944
> email: E.Bryant@bton.ac.uk
>
>
>
> MPF is a weighted average frequency in which each frequency component, f,
> is weighted by its power, P. (eg. P1 is the power of f1). Thus
>
> Equation 1
> MPF = (f1*P1+f2*P2+ ... + fn*Pn) / (P1 + P2 + ... + Pn)
>
> ie. the MPF is obtained by summing the (frequency times power) of the
> components and dividing by the sum of the powers. This is a straight
> forward parameter but a potential confusion arises from the definition of
> the power used in the Equation 1.
>
> In normal use, P is taken to be proportional to (V*V)max. This definition
> is based on the electrical origin of this type of analysis, since power in
> an (alternating) electrical signal is proportional to (V*V)max (and the
> resistence which is the same for each component and so may be ignored).
>
> So the power P1 at frequency f1 is proportional to (V*V)max,1 or more
> generally the power Pi is proportional to (V*V)max,i. Hence this
> "electrical" MPF is evaluated from:
>
> Equation 2
> MPF (electrical) = (f1*[V*V]max,1 + f2*[V*V]max,2 + ... + fn*[V*V]max,n) /
> ([V*V]max,1 + [V*V]max,2 + ... + [V*V]max,n)
>
> However, as stressed above, the voltage signal, V (t) is an electrical
> analogue of the original mechanical motion, x (t). The DFT spectrum of
> the mechanical time-domain signal would comprise a graph of the vibration
> amplitude, A, against frequency f for each of the mechanical oscillation
> components. Eg. A1 is amplitude at frequency f1 or more generally Ai is
> amplitude at frequency fi.
>
> Equation 3
> x = A sin (2*pi*f*t)
>
> The power required to maintain the oscillation given by Equation 3 is
> proportional to (Ai*fi)^2 and the electrical analogue of this is
> (fi*Vmax,i)^2. Therefore if the MPF of the mechanical motion is required,
> it should be evaluated from:
>
> Equation 4
> MPF (mechanical) = (f1*[f1*Vmax,1]^2 + f2*[f2*Vmax,2]^2 + ... +
> fn*[fn*Vmax,n]^2) / ([f1*Vmax,1]^2 + [f2*Vmax,2]^2 + ... + [fn*Vmax,n]^2)
>
> Equation 4 will, in general, give a different value for MPF from Equation
> 2.
>
>
>
>
>
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