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Integer Arithmetic

This example shows how to perform arithmetic on integer data representing signals and images.

Load Integer Signal Data

Load measurement datasets comprising signals from four instruments using 8 and 16-bit A-to-D's resulting in data saved as int8, int16 and uint16. Time is stored as uint16.

load integersignal

% Look at variables
whos Signal1 Signal2 Signal3 Signal4 Time1
  Name            Size            Bytes  Class     Attributes

  Signal1      7550x1              7550  int8                
  Signal2      7550x1              7550  int8                
  Signal3      7550x1             15100  int16               
  Signal4      7550x1             15100  uint16              
  Time1        7550x1             15100  uint16              

Plot Data

First we will plot two of the signals to see the signal ranges.

plot(Time1, Signal1, Time1, Signal2);
grid;
legend('Signal1','Signal2');

Figure contains an axes object. The axes object contains 2 objects of type line. These objects represent Signal1, Signal2.

It is likely that these values would need to be scaled to calculate the actual physical value that the signal represents, for example, Volts.

Process Data

We can perform standard arithmetic on integers such as +, -, *, and /. Let's say we wished to find the sum of Signal1 and Signal2.

SumSig = Signal1 + Signal2; % Here we sum the integer signals.

Now let's plot the sum signal and see where it saturates.

cla;
plot(Time1, SumSig);
hold on
Saturated = (SumSig == intmin('int8')) | (SumSig == intmax('int8')); % Find where it has saturated
plot(Time1(Saturated),SumSig(Saturated),'rd')
grid
hold off

Figure contains an axes object. The axes object contains 2 objects of type line. One or more of the lines displays its values using only markers

The markers show where the signal has saturated.

Load Integer Image Data

Next we will look at arithmetic on some image data.

street1 = imread('street1.jpg'); % Load image data
street2 = imread('street2.jpg');
whos street1 street2
  Name           Size                Bytes  Class    Attributes

  street1      480x640x3            921600  uint8              
  street2      480x640x3            921600  uint8              

Here we see the images are 24-bit color, stored as three planes of uint8 data.

Display Images

Display first image.

cla;
image(street1); % Display image
axis equal
axis off

Figure contains an axes object. The axes object contains an object of type image.

Display second image.

image(street2); % Display image
axis equal
axis off

Figure contains an axes object. The axes object contains an object of type image.

Scale an Image

We can scale the image by a double precision constant but keep the image stored as integers. For example,

duller = 0.5 * street2; % Scale image with a double constant but create an integer
whos duller
  Name          Size                Bytes  Class    Attributes

  duller      480x640x3            921600  uint8              
subplot(1,2,1);
image(street2);
axis off equal tight
title('Original');  % Display image

subplot(1,2,2);
image(duller);
axis off equal tight
title('Duller');    % Display image

Figure contains 2 axes objects. Axes object 1 with title Original contains an object of type image. Axes object 2 with title Duller contains an object of type image.

Add the Images

We can add the two street images together and plot the ghostly result.

combined = street1 + duller; % Add |uint8| images
subplot(1,1,1)
cla;
image(combined); % Display image
title('Combined');
axis equal
axis off

Figure contains an axes object. The axes object with title Combined contains an object of type image.