Deriving Equation of Matlab Sequence Graph

Discussion in 'Homework Help' started by tquiva, Sep 21, 2011.

  1. tquiva

    Thread Starter Member

    Oct 19, 2010


    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:

    Code ( (Unknown Language)):
    1. n=5; star=-10:10; f=-1/2:0.01:1/2-0.01; % Star & frequency intervals
    2. bbox=(abs(star)<=n); bbox=bbox/sqrt(sum(bbox.^2));
    3. BBOX=(2*n+1)*sinc(f*(2*n+1))./sinc(f);
    4. BBOX2=bbox*exp(-i*2*pi*star'*f);
    5. subplot(331),plot(star,bbox),xlabel('*'),ylabel('bbox[*]'),title('n=5')
    6. subplot(332),plot(f,BBOX),xlabel('f'),ylabel('BBOX(f)'),title('BBOX w/ sinc equation')
    7. subplot(333),plot(f,BBOX2),xlabel('f'),ylabel('BBOX(f)'),title('BBOX w/ exponential')
    9. cox=cos(pi*star/n).*bbox; cox=cox/sqrt(sum(cox.^2));
    10. COX2=cox*exp(-i*2*pi*star'*f);
    11. subplot(334),plot(star,cox),xlabel('*'),ylabel('cox[*]'),title('n=5')
    12. subplot(335),plot(f,COX),xlabel('f'),ylabel('COX(f)'),title('COX w/ since equation')
    13. subplot(336),plot(f,COX2),xlabel('f'),ylabel('COX(f)'),title('BBOX w/ exponential')
    15. c2ox=cos(pi*star/n).*cox; c2ox=c2ox/sqrt(sum(c2ox.^2));
    16. C2OX2=c2ox*exp(-i*2*pi*star'*f);
    17. subplot(337),plot(star,cox),xlabel('*'),ylabel('c2ox[*]'),title('n=5')
    18. 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?