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Informatik 4
Lab 1
Define size of 20 radius vectors
2. DCT transformation
3. Create Microsoft Excel spreadsheet
4. Create graphical representation for x(u)
1.
Laboratory Exercise Overview
A discrete cosine transform (DCT) expresses a
sequence of finitely many data points in
terms of a sum of cosine functions oscillating
at different frequencies.
DCTs are important to numerous applications
in science and engineering, from lossy
compression of audio and images (where
small high-frequency components can be
discarded), to spectral methods for the
numerical solution of partial differential
equations.
DCT
In particular, a DCT is a Fourier-related
transform similar to the discrete Fourier
transform (DFT), but using only real
numbers.
DCT
(xc,yc)
Ri 
xc  xi    yc  yi 
i  1,2,.., n
Radius Vectors
2
2
N 1

2
 2i  1u  
xu  
  ri  cos 


N  i 0
 2N  
1 N 1
x0  
ri 

N i 0
u  1,2,..., N  1
N – total number of coefficients
u – frequency spectrum index
DCT
Excel Step 1
xu  
2  N 1
 2i  1u  
  ri  cos 


N  i 0
 2N  
1 N 1
x0  
ri 

N i 0
u  1,2,..., N  1
X(0) =(1/SQRT(C2))*SUM(B2:B21)
X(1) =B2*COS(((2*$D2+1)*$L$24*180)/(2*$C$2))
pi=180
Excel Step 2
X(i)norm =F2/$F$2
Excel Step 3
1.5
1.5
1.5
1
1
1
0.5
0.5
0
0
0.5
0
-0.5
1
3
5
7
9 11 13 15 17 19
-0.5
1 3 5 7 9 11 13 15 17 19
-0.5
1.5
1.5
1.5
1
1
1
0.5
0.5
0
0
0.5
0
-0.5
1
3
5
7
9 11 13 15 17 19
-0.5
1 3 5 7 9 11 13 15 17 19
Final Graphs
-0.5
1 3 5 7 9 11 13 15 17 19
1 3 5 7 9 11 13 15 17 19
DCT parametrical featured description is
not rotation and translation invariant.
 DCT parametrical featured description is
scale invariant after applying
normalization.

Conclusion