7 For xn 1102 51 where x0110 do the following problems a Obt

7. For x[n] =110,-2, 5,-1), where x[01-10, do the following problems a) Obtain the DCT, XpCT[k] (Do not use MATLAB) b) Obtain the DFT, XLNT (You may use MATLAB) c) Seeing the DCT and DFT, what\'s big difference between DCT and DFT? e next problem(s) addresses the following course learning objective(s): Apply DFS and IDFS Understand the relationship between DFT and DFS. 8. For the given x[n], do the following problems. 21 . 0 a) Obtain the DFs, X[k], and draw | X(k]|. (Do not use MATLAB) b) Obtain the DFT of xlnl, X[k], where x[n]-13,2,1) is one period of the given n Seeing the DFS of between DFS and DFT. c) n] and DFT of x[n], explain the relationship

Solution

7.

(a)

DCT

>> x=[10 -2 5 -1];
>> y=dct(x)

y =

    6.0000    5.2919    3.0000    7.5495

(b)

DFT

>> f=fft(x)

f =

12.0000             5.0000 + 1.0000i 18.0000             5.0000 - 1.0000i

(c)

DCT is purely real and DFT is complex.