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Informatik 4 Lab 1

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Laboratory Exercise Overview 1. Define size of 20 radius vectors 2. DCT transformation 3. Create Microsoft Excel spreadsheet 4. Create graphical representation for x(u)

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DCT 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.

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DCT In particular, a DCT is a Fourier-related transform similar to the discrete Fourier transform (DFT), but using only real numbers.

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Radius Vectors (x c,y c )

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DCT N – total number of coefficients u – frequency spectrum index

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Excel Step 1

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Excel Step 2 X(0) =(1/SQRT(C2))*SUM(B2:B21) X(1) =B2*COS(((2*$D2+1)*$L$24*180)/(2*$C$2)) pi=180

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Excel Step 3 X(i)norm =F2/$F$2

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Final Graphs

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Conclusion DCT parametrical featured description is not rotation and translation invariant. DCT parametrical featured description is scale invariant after applying normalization.

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