# Deriving Equation of Matlab Sequence Graph

#### tquiva

Joined Oct 19, 2010
176
Problem:

I created the three sequences for this problem: bbox[*], cox[*], c2ox[*] along with their Fourier transforms. The problem is asking for me to find the equation of the Fourier transforms for cox[*] and c2ox[*], which is somehow similar to the one in the Fourier pair of the given problem.

So far, here's my Matlab code:

Rich (BB code):
n=5; star=-10:10; f=-1/2:0.01:1/2-0.01; % Star & frequency intervals
bbox=(abs(star)<=n); bbox=bbox/sqrt(sum(bbox.^2));
BBOX=(2*n+1)*sinc(f*(2*n+1))./sinc(f);
BBOX2=bbox*exp(-i*2*pi*star'*f);
subplot(331),plot(star,bbox),xlabel('*'),ylabel('bbox[*]'),title('n=5')
subplot(332),plot(f,BBOX),xlabel('f'),ylabel('BBOX(f)'),title('BBOX w/ sinc equation')
subplot(333),plot(f,BBOX2),xlabel('f'),ylabel('BBOX(f)'),title('BBOX w/ exponential')

cox=cos(pi*star/n).*bbox; cox=cox/sqrt(sum(cox.^2));
COX2=cox*exp(-i*2*pi*star'*f);
subplot(334),plot(star,cox),xlabel('*'),ylabel('cox[*]'),title('n=5')
subplot(335),plot(f,COX),xlabel('f'),ylabel('COX(f)'),title('COX w/ since equation')
subplot(336),plot(f,COX2),xlabel('f'),ylabel('COX(f)'),title('BBOX w/ exponential')

c2ox=cos(pi*star/n).*cox; c2ox=c2ox/sqrt(sum(c2ox.^2));
C2OX2=c2ox*exp(-i*2*pi*star'*f);
subplot(337),plot(star,cox),xlabel('*'),ylabel('c2ox[*]'),title('n=5')
subplot(339),plot(f,COX2),xlabel('f'),ylabel('C2OX(f)'),title('C2OX w/ exponential')
I know that:

Therefore, I figure... if I implement that equation for the two sequences (cox and c2ox), then I can perhaps find their Fourier equations. But then, I remembered that my code is numeric, so I will receive a number.
Now, I am completely confused. I don't think there woud be a way to make this into symbolic.

What other option(s) would I have to derive the equations for the Fourier transforms of cox and c2ox?

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