Basic signal processing - Biomedical Engineering Desk Reference - page 92

% Plots Figure 2.4.12
%
load Hr_pre

% Pre-meditative HR

load Hr_med % Meditative HR

%
% Calculate the averages and standard deviations
Avg_pre ¼ mean(hr_pre)

% Average HR, normal

SD_pre ¼ std(hr_pre) % Standard deviation, normal

Avg_med ¼ mean(hr_med) % Average and std

SD_med ¼ std(hr_med) % HR meditative

%
% Plot the heart rate data. Label axes
subplot(1,2,1);
plot(t_pre,hr_pre,'k'); % Plot normal HR data

xlabel('Time (sec)');ylabel('HR (beats/min)');
axis([t_pre(1) t_pre(end) 0 120]);
title('Preliminay HR');
subplot(1,2,2);
plot(t_med,hr_med,'k');

% Plot meditative HR data

xlabel('Time (sec)'); ylabel('HR (beats/min)');
axis([t_med(1) t_med(end) 0 120]);
title('Meditative HR')

Analysis: The program is a straightforward application of
routines mean and std. The var routine could have been
used if the variance was desired. In the plotting section,
the axis routine was used to scale the vertical axis to be
between 0.0 and 120 beats per minute. Because the time
variables had different beginning and end times, the time
limits were specified using the time array (t_pre or
t_med) endpoints. (Recall that MATLAB is case sensi-
tive.) The MATLAB files Hr_pre and Hr_med contain
variables: hr_pre, t_pre, hr_med, and t_med.
Results:

multiple sensors, but in many biomedical applications,
the multiple observations come from repeated responses
to the same stimulus. In ensemble averaging, a group, or
ensemble, of time responses is averaged together on
a point-by-point basis; that is, an average signal is
constructed by taking the average, for each point in time,
over all signals in the ensemble. A classic biomedical
engineering example of the application of ensemble av-
eraging is the visual evoked response (VER) in which
a visual stimulus produces a small neural signal embed-
ded in the EEG. Usually this signal cannot be detected in
the EEG signal, but by averaging hundreds of observa-
tions of the EEG, time-locked to the visual stimulus, the
visually evoked signal emerges.
There are two essential requirements for the appli-
cation of ensemble averaging for noise reduction: the
ability to obtain multiple observations and a reference
closely time-linked to the response. The reference shows
how the multiple observations are to be aligned for av-
eraging. Usually a time signal linked to the stimulus is
used. An example of ensemble averaging is given in Ex-
ample 2.4.8.

Premeditative Meditative

Average heart rate
(beats/min)

66.5 81.33

Standard deviation
(beats/min)

5.36 9.35

In this subject, meditation increased the heart rate by
about 22% and the standard deviation by almost 75%, not
a result that might be anticipated by this Yoga-based
meditation. (See the PhysioNet database for more details
on the meditative conditions.)

Example 2.4.8: Find the average response given a number
of individual responses from the vergence eye movement
system. The vergence eyemovement systemis responsible
for turning the eye inward to view a near target. These
responses are stored in MATLAB file vergence.mat.

2.4.4.2 Ensemble averaging

Equation 2.4.22 indicates that averaging can be a simple
yet powerful signal-processing technique for reducing
noise when multiple observations of the signal are
possible. Such multiple observations could come from

Solution: Use the MATLAB averaging routine mean.If
this routine is given a matrix variable, it averages each
column. Hence, if the various signals are arranged as rows