Faster Convolution with Separability Property in Multi-dimensional Signals

Topic: Digital image processing. 

Consider a 2D signal (or impulse response of 2D filter) with rect-shaped.

 This 2D rect signal is separable. It can be represented as dot-product of two independent 1D signals.
As well an impulse signal is also separable.

Basic JPEG Compressing/Decompressing Simulation

Standard JPEG compression uses (1) 8x8 Discrete Cosine Transform, (2) quantization based on certain luminance + chrominance tables, and (3) entropy-encoding (Huffman coding).
Here, I'm using OpenCV (Python) to simulate DCT + quantization + IDCT, without Huffman coding.