This Extra Bit shows the computer code, written in the widely used language MatLab, for making the two examples of amplitude envelopes in the text. A lot of the examples in this book were made using MatLab, but we've used a number of other software programs as well. We're including this to give you a look "under the hood" at how one goes about making these kinds of pictures. Try to read thru it and get some idea of how one does this sort of thing.

Comments are preceded by the percent sign (%). The code itself is in red.

% MatLab Code:
% Take the average and peak envelopes of an input signal, and plot all three together
% Expects a .wav soundfile as input
% usage: ampenv('myfile.wav')

% this beginning part just defines the function to be used in MatLab, takes a "wav" soundfile as an input, and spits out a % graph

function [ampenv] = ampenv( file );

clf % clears the graphic screen

% read in the soundfile, into a big array called y
y = wavread( file );

% normalize y, that is, scale all values to its maximum. Note how simple it is to do this in MatLab.
y = y/max(abs(y));

% if you want to hear the sound after you read it in, uncomment this next line. Sound just plays a file to the speaker.
%sound(y, 44100);

% initialize peak and average arrays to be the same as the signal. We're keeping three big arrays, all of the same length.
averageenv = y;
maxenv = y;

% Set the window lengths directly, in number of samples. Generally, the average should be smaller than the peak, since it
% will tend to flatten out if it gets too big. These two numbers can be played with to vary what the pictures will look like. Note that we keep two different windowsizes, so that we can have different kinds of resolution for peak and average charts.
averagewindowsize = 512;
peakwindowsize = 1000;

% go thru the input signal, taking an average of the previous, averagewindowsize number of samples, and store that in the %current place in the average array. We do this by having a loop that starts at the end of the first window, and goes to the % % end of the soundfile, indicated by length(averagenv). The MatLab command sum takes some range of a vector, and gives % you back the sum (pretty cool, huh?)
for k = averagewindowsize:length(averageenv)
runningsum = sum(abs(y(k-averagewindowsize-1:k)));
averageenv(k) = runningsum /averagewindowsize ;
end

% go thru the input signal, taking the maximum value of the previous peakwindowsize number of samples. we do this in the same way as we did the average, but now we use max instead of sum.
for k = peakwindowsize:length(maxenv)
maxenv(k) = max(y(k-peakwindowsize:k));
end

% plot the three "signals", the original in the color cyan, the peak in magenta, the average in blue. the command hold on invokes the ghost of Sam and Dave to allow us to overprint on the current graph, so that we can show all three lines together. the rest of this is just MatLab graphics instructions (titles, labels, axes, etc.). The colors are the letters in single quotes.
plot(y, 'c')
hold on
plot (maxenv, 'm')
hold on
plot(averageenv, 'b')
title('Monochord: Signal, Average Signal Envelope, Peak Signal Envelope')
xlabel('sample number')
ylabel('amplitude (-1 to 1)')
legend('original signal', 'peak envelope', 'running average envelope', 0)