> 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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