%	Unit step function defined as 0 for input argument values 
%	less than zero, 1/2 for input argument values equal to zero,
%	and 1 for input argument values greater than zero.  Works
%	for vectors and scalars equally well.  

function y = u(t)
	zro = t == 0 ; pos = t > 0 ; y = zro/2 + pos ;

%	Function to compute the ramp function defined as 0 for 
%	values of the argument less than zero and the value of 
%	the argument for arguments greater than or equal to zero.
%	Works for vectors and scalars equally well.

function y = ramp(t)
	y = t.*(t >= 0) ;

%	Rectangle function.  Uses the definition of the rectangle
%	function in terms of the unit-step function.  Works on 
%	vectors or scalars equally well.

function y = rect(t)
	y = u(t+0.5) - u(t-0.5) ;

%	Function to compute the triangle function.  Uses the definition
%	of the triangle function in terms of the ramp function.  Works
%	for vectors and scalars equally well.

function y = tri(t)
	y = ramp(t+1) - 2*ramp(t) + ramp(t-1) ;

%	Function to compute sinc(t) defined as sin(pi*t)/(pi*t).
%	Works for vectors or scalars equally well.  This function
%	may be intrinsic in some versions of MATLAB.

%	Function to compute values of the Dirichlet function.
%	Works for vectors or scalars equally well.  
%
%	x = sin(N*pi*t)/(N*sin(pi*t))
%
function x = drcl(t,N)
	x = diric(2*pi*t,N) ;

%	Function to implement the Dirichlet function without using the 
%	MATLAB diric function.  Works for vectors or scalars 
%	equally well.  
%
%	x = sin(N*pi*t)/(N*sin(pi*t))
%
function  x = drcl(t,N),
	num = sin(N*pi*t) ; den = N*sin(pi*t) ;
	I = find(abs(den) < 100*eps) ;
	num(I) = cos(N*pi*t(I)) ; den(I) = cos(pi*t(I)) ;
	x = num./den ;

%	Function to generate the discrete-time impulse function defined as
%	one for input integer arguments equal to zero and zero otherwise. 
%	Returns "NaN" for non-integer arguments.  Works for vectors and
%	scalars equally well.
%
%	function y = impD(n)

function y = impD(n)
	y = double(n == 0) ;		%	Impulse is one where argument 
						%	is zero and zero otherwise
	ss = find(round(n)~=n) ;	%	Find non-integer values of "n"
	y(ss) = NaN ;			%	Set corresponding outputs to 
						%	"NaN"

%	Unit sequence function defined as 0 for input integer argument 
%	values less than zero, and 1 for input integer argument values 
%	equal to or greater than zero.  Returns "NaN" for non-integer 
%	arguments.  Works for vectors and scalars equally well.
%
%	function y = uD(n)

function y = uD(n)
	y = double(n >= 0) ;		%	Set output to one for non-
						%	negative arguments
	ss = find(round(n)~=n) ;	%	Find all non-integer "n's"
	y(ss) = NaN ;			%	Set the corresponding outputs 
						%	all to "NaN"

%	Unit discrete-time ramp function defined as 0 for input integer 
%	argument values equal to or less than zero, and "n" for input 
%	integer argument values greater than zero.  Returns "NaN" for non-%	integer arguments.  Works for vectors and scalars equally well.
%
%	function y = rampD(n) 

function y = rampD(n)
	pos = double(n>0) ;		%	Set output to "n" for positive
	y = n.*pos ; 			%	"n"
	ss = find(round(n)~=n) ;	%	Find all non-integer "n's"
	y(ss) = NaN ;			%	Set the corresponding outputs 
%	all to "NaN"

%	Discrete-time rectangle function defined as 1 for input integer 
%	argument values equal to or less than "W" in magnitude and zero 
%	for other integer argument values.  "W" must be an integer.  
%	Returns "NaN" for non-integer input values.
%
%	y = rectD(W,n)

function y = rectD(W,n)
	if W == round(W),
		y = double(abs(n)<=abs(W)) ;	%	Set output to one if 
						 	%	|n|<=|W|and zero 
						 	%	otherwise
		ss = find(round(n)~=n) ; 	%	Find all non-integer 
						 	%	"n's"
		y(ss) = NaN ;		 	%	Set the corresponding 
						 	%	outputs all to "NaN"
	else
		disp('In rectD, width parameter, W, is not an integer') ;
	end

%	Discrete-time periodic impulse function defined as 1 for input 
%	integer argument values equal to integer multiples of "N" and 0 
%	otherwise.  "N" must be an integer. Returns "NaN" for non-integer %	input values.  Works for vectors and scalars equally well.
%
%	function y = impND(N,n)

function y = impND(N,n)
	if N == round(N),
y = double(n/N == round(n/N)) ;	%	Set output to one 
%	for all n's which 
%	are integer
%	multiples of N 
%	and zero otherwise
		ss = find(round(n)~=n) ;		%	Find all non-
%	integer n's"
		y(ss) = NaN ;				%	Set the 
%	corresponding 
%	outputs all to 
%	"NaN"
	else
		disp('In impND, period parameter, N, is not an integer') ;
	end