# Choosing A & alpha complex constants for a sequence

#### tquiva

Joined Oct 19, 2010
176
Problem: I've been working on this problem, but I'm not entirely sure if I did it correctly since all the graphs for each instance seems the same as another. Here's my Matlab code. Any suggestions or advice for part (e)? I really don't know how to find the complex constants A and alpha for x
[*]=x[-*]

Rich (BB code):
% PROBLEM 4

star=-5:0.1:5

% (a) When all components of the time sequence take only real values, the
% sequence is a real time sequence.

% To get real number from complex constants, set exponential equal to 1.
% Therefore, theta=0 for complex constant A*exp(i*theta)
A=a*exp(i*0);
alpha=b*exp(i*0);

s=A*alpha^2*heaviside(star),

plot3(star,real(s),imag(s),star,real(s),imag(s),'o')

% (b) If some of the components take complex values, it is a complex time
% sequence.

a=1; b=2;
A=a*exp(i*2);
alpha=b*exp(i*3);
s=A*alpha^2*heaviside(star),
plot3(star,real(s),imag(s),star,real(s),imag(s),'o')

plot(star,s),xlabel('*'),ylabel('s
[*]'),title('Imaginary s
[*]')

% (c) A sequence is bounded if there is a finite positive number say B such
% that the magnitudes of all the sequence components are bounded above B.

B=1;
a=2; b=3;
A=a*exp(i*2);
alpha=b*exp(i*3);
s=A*alpha^2*heaviside(star),
plot(star,s),xlabel('*'),ylabel('s
[*]'),title('Imaginary s
[*]')

% (d) If a sequence has finite energy, then the parameters must have
% parameters strictly less than unity.

a=1; b=1/2;
A=a*exp(i*2)
alpha=b*exp(i*3)
s=A*alpha^2*heaviside(star),
plot(star,s),xlabel('*'),ylabel('s
[*]'),title('Imaginary s
[*]')

% (e) An even sequence is a sequence where x
[*]=x[-*]