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Here is the small experiment I was able to conduct on my Debian system. I crafted two small $8 \times 8$ JPEG files again: white: () black: () I used the following commands: % convert -size 8x8 -depth 8 xc:white white.pgm % convert -size 8x8 -depth 8 xc:black black.pgm then: % cjpeg -sample 1x1 -quality 100 -grayscale -outfile white.jpg white.pgm % cjpeg -...

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The transformation defined in the book (Cosine and Sine) are based on symmetric or anti symmetric functions. The implied information is that when we use them to apply convolution they will apply Circular Convolution (This is true to both) while one will apply it with Symmetric and the either anti symmetric. When we use it? Whenever we analyze signals using ...

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i know that frequency of A * cos (Bx - C) + D is B / 2pi Exactly. So let's take the DCT-II: $$X[k]:=\sum_{n=0}^{N-1} x_n \cos \left[\, \tfrac{\,\pi\,}{N} \left( n + \frac{1}{2} \right) k \, \right] \qquad \text{ for } ~ k = 0,\ \dots\ N-1$$ and look at the argument of the cosine. \begin{align} \frac\pi N\left( n+\frac12 \right) k &= \underbrace{\pi ...

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