The first eight pixels of a scanned image are as follows: $f=[50,60,55,65,68,62,67,75]$. Calculate the DFT and DCT coefficients of the signal. Retain the 5 largest magnitude coefficients in both cases, and drop the three lowest magnitude coefficients. Reconstruct the signal by calculating inverse transforms, and determine which transform reconstructs the edge better? Compare the results with those obtained in Example 8.4.