% ECE 1250 Lecture 6

%-------------------------------------------------------------------------------
% Array Processing, Fourier Series, and Plot Labeling
%-------------------------------------------------------------------------------
% Fourier theory says any  waveform may be approximated as a sum of
%  sinusoids of different frequencies, amplitudes, and phase shifts.

% Ex: Fourier series for square wave, first three terms.
% First we create a vector of time values.
>> t=(1:1000)/8000;   % Divide by 8000 to match sampling rate for sounds

% Set the frequency of the square wave we want to approximate at 100 Hz.
>> sqfreq = 100;

% Create sinusoids at frequencies of 100 Hz, 300 Hz, and 500 Hz.
% Note that f1, f3, and f5 are arrays of 1000 points each.
>> f1 = cos(2*pi*sqfreq*t);
>> f3 = (-1/3)*cos(2*pi*3*sqfreq*t);
>> f5 = (1/5)*cos(2*pi*5*sqfreq*t);

% Sum the three sinusoids.
>> y = f1 + f3 + f5;

% Start a new figure.
>> figure

% Use a bigger font than normal for labels.
>> axes('FontSize',14,'Parent',figure)  % Must be done before plot.

% Plot the y waveform as red points.
%  'r.' is a string that specifies red and dots)
>> plot(t,y,'r.')
% We get an approximation of a square wave.

% Add some nice labels.
>> xlabel('Time')
>> ylabel('Voltage')
>> title('Fourier Series for Square Wave')

% Set the endpoints of the axes 
>> axis([0, 1000/8, -2, 2])   % Format is [xmin, xmax, ymin, ymax]

% It sounds kind of grungy
>> sound(y)







%-------------------------------------------------------------------------------
% 3-D plots using meshgrid()
%-------------------------------------------------------------------------------
% What does magic square look like when plotted as a surface?
% We use the meshgrid() function to generate (x,y) points on a regular grid.
% Instead of creating ordered pairs, meshgrid() puts all the x values in one
%  array and all the y values in another array.
[xx,yy] = meshgrid([1:15],[1:15]);

% Now we create the z values.  Normally z is a function of xx and yy.
% Here, however, we create a magic square that is 15 x 15 in size, so
%  our xx and yy will correspond to row and column indices.
z = magic(15);

% Now we make our 3-D plot as a lit surface.
surfl(xx,yy,z)

%-------------------------------------------------------------------------------
% 3-D Plot of a sinusoid
%-------------------------------------------------------------------------------
% Create a mesh grid on a square [-1,1] x [-1,1] with 15 pts in each direction.
x1range = [-1,1];
x2range = [-1,1];
npts = 15;
x1pts = x1range(1):(x1range(2)-x1range(1))/(npts-1):x1range(2);
x2pts = x2range(1):(x2range(2)-x2range(1))/(npts-1):x2range(2);
[xx,yy] = meshgrid(x1pts,x2pts);

% Compute a cos of x+y.
zz = cos(2*pi*2*(xx+yy));

% Make a surface plot.
surfl(xx,yy,z)

%-------------------------------------------------------------------------------
% Array Processing and 3-D Plotting
%-------------------------------------------------------------------------------
bumps.m    This script file creates bumps and sums them to create a surface.

% Coming up:
% Matrix inverses, pseudoinverses
% Programming: control flow, functions