Maximum and minimum points of a dataset in MatLab

Question

Hi I'm trying to find a way to create a matrix in MatLab with only the maximum and minimum values of an exercise repeated over a 30 second period.

For example, if I had the dataset:

data = [1 3 5 7 9 6 4 2 3 6 8 10 7 6 4 2 1]

My wanted outcome would be:

output = [1 9 2 10 1]

the function would only plot the peak values of a constantly changing waveform.

The code I've tried is as follows:

size = length(data);    %Get the length of the dataset 
x = 1;                  %Set a counter value
maxplot = 0;            %Default, a maximum value has not yet been plotted

for x = 1:size-1
    a1 = data(1,x);     %Get two adjacent samples of the dataset
    a2 = data(1,x+1);

    v = 1;  %Set the initial column for the max points matrix

    while maxplot == 0
        if a1 > a2
            max(v,1) = a1;
            v = v + 1;
            maxplot = 1;
        end
    end

    if a1 < a2
        maxplot = 0;    
    end
end 

Thanking whoever replies in advance,

Jared.

Answer 1

You could use something like this:

function Y = findpeaks(X)
    deltas = diff(X);
    signs = sign(deltas);
    Y = [true, (signs(1:(end-1)) + signs(2:end)) == 0, true];

findpeaks will return a logical array of the same length as its input X array. To extract the marked values, just index by the logical array.

For example,

data = [1 3 5 7 9 6 4 2 3 6 8 10 7 6 4 2 1];
peaks = data(findpeaks(data))

Should output:

peaks =
    1    9    2   10    1

This function does not do anything special to cope with repeated values in the input array. I leave that as an exercise for the reader.

Answer 2

This version isn't as pretty as John's, but it doesn't lose peaks when there are flat parts:

function peaks = findpeaks(data)
% Finds the peaks in the dataset

size = length(data);    %Get the length of the dataset 
x = 1;                  %Set a counter value
peaks = data(1,1);      %Always include first point

if size == 1  %Check for sanity
    return
end

lastdirection = 0;      %Direction of change

directions = sign( diff(data) ); %Directions of change
                                 % between neighboring elements

while x < size
    % Detect change in direction:
    if abs( directions(x) - lastdirection ) >= 2
        peaks = [peaks, data(1,x)];
        lastdirection = directions(x);
    else
        % This is here so that if lastdirection was 0 it would get
        % updated
        lastdirection = sign( lastdirection + directions(x) );
    end
    x = x+1;
end

peaks = [peaks, data(1,size)];
end