LAB 2, 02/05/14
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1.	MATLAB distinguishes between

	- matrix operations (which follow the standard rules of linear
	  algebra)

	and

	- array operations (which are performed on individual elements
	  of an array, or between corresponding elements of different
	  arrays of the same size)

	Array operators that differ from their matrix counterparts are
	generally preceded by . (period)

	For example, if A and B are matrices of size m*n, then

		A  *  B  (matrix product) is defined only when m=n

		A.' * B  (also matrix product) is always defined, by
			virtue of the transposition of A

		A  .* B  (array product) is always defined, and produces
			a new array of the same size

	Thus
		a = 1:4

		b = 1:2:7

		a*b         % undefined

		a.'*b       % valid

		a*b'        % dot product of a and b

		a.*b        % same size as a and b


2.	The commands 

		PLOT and STEM

	were introduced earlier, in basic plotting applications. MATLAB
	has diverse 2-D graphing capabilities.  The PLOT command, in
	particular, can be used in a variety of formats.

	Consider three sinusoids, each spanning 1000 points in the time 
	interval [0,2) sec:

		Ts = 0.002;          % spacing, or sampling period

		t = 0:Ts:(2.0-Ts);   % discrete time axis

		T1 = 1/5; q1 =   .2; % period, phase (sinusoids 1,2,3)
		T2 = 1/3; q2 = -1.8;
		T3 = 1/4; q3 =  2.5;

		A1 = 1.0; A2 = 2.0; A3 = 3.0; % amplitudes

		x1 = A1*cos(2*pi*t/T1 + q1) ;
		x2 = A2*cos(2*pi*t/T2 + q2) ;
		x3 = A3*cos(2*pi*t/T3 + q3) ;

	Does the time interval [0,2) contain a whole or fractional number
	of periods of each sinusoid?


3.	Basic plot of x1 (no time axis):

		plot(x1)

	With the correct time axis:

		plot(t,x1)

	Add a grid:

		grid

	(To adjust the grid density, click EDIT and then AXIS PROPERTIES on
	the figure window. Change the tick spacing for the X and Y axes.)

	Clear the figure window:

		clf

	Plot x1 in red:

		plot(t,x1,'r')

	Use the HOLD function to hold the current plot and overlay a plot of
	x2 in black:

		hold		% hold turned on
		plot(t,x2,'k')

	Continue holding (no action needed) and overlay a plot of x3 in
	a dotted blue line:

		plot(t,x3,'b:')

	You can also plot all three graphs using the same PLOT command:

		hold		% hold turned off (alt.: just use CLF)
		plot(t,x1,t,x2,t,x3)


4.	Change the properties of the axes using the AXIS command:

		axis square

		axis fill

		axis([0,2,-4,4])

		axis([-1,3,-4,4])

		axis tight

	These properties can also be changed using EDIT > AXES PROPERTIES
	in the figure window.  The same holds for graph and axis labels: they
	can be specified in the figure window (as axes properties), or in
	the command window using

		XLABEL, YLABEL and TITLE

	For example:

		xlabel('Time')		% Quotes denote character string
		
		ylabel('Voltage')
	
		title('Three Sinusoids')


5. 	A sinusoid and its exponentially faded version:


		f = 660/8192;       % frequency parameter in cycles/sample
		N = 16384;          % number of samples
		r = 4;              % exponential decay parameter

		n = 0:N-1;          % discrete time axis

		x = cos(2*pi*f*n);  % thus w = 2*pi*f

		e = exp(-r*n/N);    % like cos(.), exp(.) operates on
		                    % each element of the array

		y = x.*e;           % array multiplication

		plot(x)             % many periods of the sinusoid; zoom in!

		plot(y)             % note exponentially decaying envelope


6.	The SUBPLOT function allows multiple graphs to be displayed on a grid
	in the same figure window.  This is accomplished by preceding each PLOT
	(or STEM, BAR, etc.) command by the statement

		SUBPLOT(NROWS,NCOLS,ORDER)

	where NROWS is the number of rows, NCOLS is the number of columns and 
	i=1,2,... is the ORDER in which the graph is displayed on the grid.
	Try out

		clf

		subplot(2,1,1), plot(x(1:200))

		subplot(2,1,2), plot(y(1:200))