Given the following portion from an $88$ block from an image after the Discrete Cosine Transform has been

applied.

$2\mathrm{.}1$ What is the result of the quantization step of the JPEG compression method assuming that a constant

quantization value of $32$ is used.

Note. JPEG uses a quantization table with different values varying according to the exact coefficient to

approximate. Here, we just use one value equal to $32$ for all; DCT coefficients are divided and round down.

$2\mathrm{.}2$ What is the resulting one$-$dimensional sequence after applying the zig$-$zag scanning to the quantized

block?

$2\mathrm{.}3.$ What is the resulting sequence after applying run length encoding $($RLE$)$ to the zig$-$zag step's output?

RLE: Replace repeating values with pairs composed of their value plus number of repetitions in the

sequence.

$2\mathrm{.}4$ What is the resulting block of coefficients after de$-$quantization?