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When DCT is defined by a matrix, then this matrix contains the necessary information to build the basis functions. Suppose that $I$ is your $8\times8$ block, and $D$ a real $8\times8$ matrix for a 1D DCT (with column-wise vectors). Then $D^TI$ applies the DCT on columns, and $ID$ does it on rows. Thus, a 2D DCT yields a $8\times8$ matrix $C$ of ...


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My knowledge of DFT is not very advanced but from I understand it is similar to other frequency domain transforms like Fourier or Radon. The frequencies that you want to check against have already been defined and "standardized". The way that you sum those different frequencies create frequencies that resemble the one you are trying to recreate. So to answer ...


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Q1: You should ask yourself if $$\frac{z}{3z^2 - 4z + 1}\stackrel{?}{=}\frac{\frac 3 2}{z-1} - \frac{\frac 1 2 }{z-\frac 1 3}$$ really holds. You'll find out that you forgot to scale correctly. Q2: There is no reason to consider $X(z)/z$ instead of $X(z)$ in this case. And concerning your question about the anti-causal sequence, a multiplication by $z^{-...


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