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View Full Version : Summary: [BIOMCH-L] Resampling data at different sampling rates

Chris Kirtley
05-19-2004, 09:43 PM
Deart all resamplers,

Thanks to everyone for the responses to my query about resampling. Most
people suggested the MATLAB function, and I forgot to ask people not to
refer to MATLAB. Whilst I agree that it's a good solution, I personally
prefer to know what algorithm I am using - more intellectually
satisfying and perhaps safer. But it's a personal bette noire of mine
:-)

Some people did suggest algorithms involving linear interpolation. I
have used these in the past with good results. This necessarily involves
increasing the sampling rate of the kinematics to equal that of the
force data (which will result in big, clumsy files) - does anyone know
if it is possible to go the other way (i.e. reduce the sampling rate)?
Or, in other words, does anyone know how MATLAB does it?

I should also have said that I was hoping for a solution that could be
implemented in Excel - perhaps this is impossible?...

Chris
--- responses begin...
Chris,

I did some work on this matter a few years back when trying to
determine joint moments in sprinting from kinematic data collected at
50Hz and GRF data collected at 1000Hz. We hypothesised that the GRF
rather than segmental accelerations would be the major cause of joint
moment. Thus, rather than loose anything from our GRF data, we
interpolated our kinematic data using quintic splines. We tested our
hypothesis by recalculating moment data with segmental accelerations
set to zero. You can read the specific details in:

Johnson MD and Buckley JG. (2001) The Biomechanics of Sprinting.
Post-start Performance. Journal of Sport Sciences, 19:263-272.

hope this helps

John Buckley, PhD
Research Associate (biomechanics)
Dept of Optometry
---
Chris,

I use the attached MATLAB function, written by a friend of mine, to
evenly sample signals. I think
it may do what you want.

Eric Westervelt
%************************************************* **********************

%
% CONVERTS A RANDOMLY SAMPLED SIGNAL SET INTO AN EVENLY SAMPLED
% SIGNAL SET (by interpolation)
%
% By : Haldun KOMSUOGLU
% Start : 07/23/1999
% Last : 07/23/1999
% Statue : Neural Model Research Material
%
% Inputs:
% t : A column vector that contains the time values for the

% corresponding computed state trajectory points
% x : A matrix in which each row is a state value on the
% solution trajectory that corresponds to the time
value in
% vector t with the same row value. Format of each row:

% row = [x1 x2 ... xN]
% Fs: The sampling frequency (1/sec) for the evenly sampled

% set to be generated.
%
% Outputs:
% Et : Even sampling instants. This is a column vector in
the
% same format with "t".
% Ex : A matrix of the same form with "x" that contains the

% state values corresponding to the time instants in
Et
%
%************************************************* **********************

function [Et, Ex] = even_sample(t, x, Fs);

% Obtain the process related parameters
N = size(x, 2); % number of signals to be interpolated
M = size(t, 1); % Number of samples provided
t0 = t(1,1); % Initial time
tf = t(M,1); % Final time
EM = (tf-t0)*Fs; % Number of samples in the evenly sampled case with
% the specified sampling frequency
Et = linspace(t0, tf,round(EM))'; % ROUND ADDED TO GET TRULY EVEN
SAMPLING.

% Using linear interpolation (used to be cubic spline interpolation)
% and re-sample each signal to obtain the evenly sampled forms
for s = 1:N,
Ex(:,s) = interp1(t(:,1), x(:,s), Et(:,1));
end
---
I have used two different solutions. One is to do linear interpolation
the equation for this is quite simple (see below). A better
solution is to use the Shannon algorithm. This gives a curvilinear fit
to the data. The following paper outlines the procedure:

Hamill, J.; Caldwell, G.E. & Derrick, T.R. (1997) A method for
reconstructing digital signals using Shannon's sampling theorem.
Journal of Applied Biomechanics, 13: 226-238.

Linear interpolation routine (in C):
(ndata = number of original data)
(normbase = number of time intervals of normalized data = number
of normalized data -1)

duration = (ndata - 1) / rate
Fx = (ndata - 1) / normbase

'Normalize the data and place in array Y.
Y(1) = data(1)
Y(normbase + 1) = data(ndata)
dx = 1.0
For j = 2 To normbase
dx = dx + Fx
ix = Int(dx)
Y(j) = data(ix) + (data(ix + 1) - data(ix)) * (dx - ix)
Next j
I have used two different solutions. One is to do linear interpolation
the equation for this is quite simple (see below). A better
solution is to use the Shannon algorithm. This gives a curvilinear fit
to the data. The following paper outlines the procedure:

Hamill, J.; Caldwell, G.E. & Derrick, T.R. (1997) A method for
reconstructing digital signals using Shannon's sampling theorem.
Journal of Applied Biomechanics, 13: 226-238.

Linear interpolation routine (in C):
(ndata = number of original data)
(normbase = number of time intervals of normalized data = number
of normalized data -1)

duration = (ndata - 1) / rate
Fx = (ndata - 1) / normbase

'Normalize the data and place in array Y.
Y(1) = data(1)
Y(normbase + 1) = data(ndata)
dx = 1.0
For j = 2 To normbase
dx = dx + Fx
ix = Int(dx)
Y(j) = data(ix) + (data(ix + 1) - data(ix)) * (dx - ix)
Next j

D. Gordon E. Robertson, Ph.D., FCSB
Professor of Biomechanics
School of Human Kinetics, University of Ottawa
Ottawa, ON, Canada, K1N 6N5
mailto:dger@uottawa.ca
+1-613-562-5800 Off: 4253 Lab: 4246 Fax: +1-613-562-5149
Webpage: http://www.health.uottawa.ca/biomech/lab
Personal: http://myprofile.cos.com/dger
--
Hi Chris,

Given that resampling data to a lower data rate is a form of
sampling,
would you be better to take the approach of upsampling the lower sample
rate data to match the faster data? I'll admit that I haven't thought
about this much but it would seem to be a much safer (data integrity
wise) method than downsampling. Upsampling both data sets also offers
the possibility of a "perfect" sample match too.
How much call is there for this sort of thing? My first guess is
that
it's relatively uncommon but maybe people just give up when faced with
the
problem.
FWIW - the C3Deditor provides upsample capabilities but I get very
few

Regards,
Edmund Cramp
--
Motion Lab Systems, Inc.
15045 Old Hammond Hwy, Baton Rouge LA 70816
Tel: +1 225 272-7364, Fax: +1 225 272-7336
---
Chris,

I collect kinematic (Polhemus) and analog data at different sampling
rates in labview. I basically time stamp each data point and then
interpolate the analog data to match the time on the kinematic data. I
use a linear interpolation scheme, but if you were worried about sharp
gradients, you could certainly use a non-linear scheme. I realize that
this is an overly simplistic approach, but it works fairly well,
especially if you don't need to differentiate your data.

Andrew Karduna
---
Dear Chris,
I am not an expert but for my research I have used resample function in
Matlab. See www.mathworks.com for more details.
Good luck and please send me resume.
Andrzej
"AS Przybyla, Anatomy"
---
Hi Chris and all, we use Matlab and it contains a RESAMPLE function.
You feed
in the data for a gait cycle and it is resampled over your selected
number of
points. so for force in stance phase you would have to look at the
number of
samples for the 60 Hz kinematic data and resample the force data over
that
number of points.
Its a suggestion!
Cheers
Cathy

Dr Cathy Holt
Lecturer in Biomechanics and Materials
Division of Materials and Minerals Engineering
Cardiff School of Engineering
PO Box 925
Newport Rd
Cardiff CF24 0YF
00 44 0(29) 2087 4533
fax 00 44 0(29) 2087 4939
http://www.engin.cf.ac.uk/whoswho/profile.asp?RecordNo=198
---
Chris,

I have two data sets (moments and power) taken for two different
groups. Of course the stance phase data is normalized to different
values - 200 and 120 respectively. To look at phase shifts between
groups, I am having to decimate to come down in sample
number, and interpolate (of sort) to come up to an in between number of
150 points. Matlab has an intrinsic that has worked well so
far. I am pasting below.....

Hope this helps. I have not had a chance to compare reduced graphs of
any real "messy" data, but my angles (ankle, knee, and hip),
moments and power figures look good.

Regards Dwight

DECIMATE Resample data at a lower rate after lowpass filtering.
Y = DECIMATE(X,R) resamples the sequence in vector X at 1/R times
the
original sample rate. The resulting resampled vector Y is R times
shorter,
LENGTH(Y) = LENGTH(X)/R.
DECIMATE filters the data with an eighth order Chebyshev Type I
lowpass
filter with cutoff frequency .8*(Fs/2)/R, before resampling.
Y = DECIMATE(X,R,N) uses an N'th order Chebyshev filter.
Y = DECIMATE(X,R,'FIR') uses the 30 point FIR filter generated by
FIR1(30,1/R) to filter the data.
Y = DECIMATE(X,R,N,'FIR') uses the N-point FIR filter.

Note: For large R, the Chebyshev filter design might be incorrect
due to numeric precision limitations. In this case, DECIMATE will
use a lower filter order. For better anti-aliasing performance, try

breaking R up into its factors and calling DECIMATE several times..

Dwight E. Waddell, Ph.D.
School of Applied Physiology
Center for Human Movement Studies
Georgia Institute of Technology
Atlanta, GA 30332-0356 USA

Office: (404) 385-1559
Fax : (404) 894-7593
---
As to your question to the Biomch-l, why not use the Resample function
in Matlab. Have a look at the enclosed figure where I took the raw data
of
an accelerometry sequence (arbitrary units) sampled at 128 Hz, and did

two resamplings at 55 and 20 Hz. Matlab chooses appropriate
anti-aliasing
filters. You can manipulate the filter coefficients which is not my
field.

Take care!

Rolf Moe-Nilssen
--
Dr. Chris Kirtley MD PhD
Associate Professor
Dept. of Biomedical Engineering
Catholic University of America
620 Michigan Ave NE, Washington, DC 20064
Tel. 202-319-6134, fax 202-319-4287
Email: kirtley@cua.edu
http://faculty.cua.edu/kirtley

In May 2004 I am at STAPS, University of Reims, France
Tel. 06-77944628

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