LAB ASSIGNMENT 3 (due 02/19/14)
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A linear filter acts on a real-valued input sequence u[n] to produce an 
output sequence v[n], where n is an integer representing discrete time.  
At time n, the output sample is given by

	v[n] =  0.5*v[n-1] - 0.4*v[n-2] + u[n]	(**)

Suppose that the input sequence u[n] is given by

	u[n] = 0 for n<0

	u[n] = (r^n)*cos(2*pi*f*n), for n>=0  (***)

where 0<r<1 and 0<=f<=1/2.  Thus u[n] is a sinusoid of decaying amplitude - 
or equivalently, an oscillating decaying exponential.

We would like to determine those values of r and f on the discrete
grid
	r = 0.01 : 0.01 : 0.99 ;

	f = 0 : 0.01 : 0.5 ;

such that v[n] is a bounded signal, i.e., there exists a finite value M 
such that v[n] is in the interval [-M,M] for all n.  Since we need to 
stop at some n, we will use the following criterion for boundedness: 
v[n] is bounded if by time n=1000, all output samples are less than 10^6 
in absolute value.  Those pairs (r,f) that pass the test are saved as
r+j*f in a vector S, which is then plotted (imaginary versus real part).

The idea is very similar to the one developed in Lab 3 for the Mandelbrot 
set. Here are some pointers:

	- Initialize both S and T to [ ] ;

	- Use two nested FOR loops to cover the (r,f) grid.

	- Use the vector vec to store the output samples produced by (***)

	- Initialize vec to [0 0] and n = 0.  In effect, (***) will be used
	  to compute output samples starting at time n = 0, assuming that
	  the outputs at times n = -2 and n = -1 were both zero.

	- Use a WHILE loop that

		- computes the current input using the formula (***)

		- computes the corresponding output sample v using (**)

		- appends v to vec

		- increments n

	   as long as the output is less than 10^6 in absolute value and
	   the size of vec does not exceed 1002.

	-  Append r+jf to S if the boundedness test is passed; otherwise
	   append r+jf to T

	-  Plot the points in S using . (point) as markers, and those
	   in T using x (x-mark).

(Hint: When programing, you may want to set the threshold value to 1.1 
instead of 10^6 to ensure your code works!)

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Submit a zip/rar package containing the following two files (use exact file
names as shown):

lastname_labhw_03.m	
        M-file containing the MATLAB code and any additional comments or
        explanations on separate lines preceded by % (comment character).
        Please put your name and student ID on the first line.

lastname_labhw_03.pdf
        Figure saved in PDF format.

The zip/rar package should be named as lastname_labhw_03.zip/rar, and 
should be uploaded from the upload link on the course lab web page 
<http://terpconnect.umd.edu/~jzsimon/enee222/lab.html>, or if not possible, 
emailed to enee222S2013@gmail.com.