Why subtract 128 before the DCT?

An 8-bit unsigned image lives in [0,255]. Centering around zero (pixel − 128) puts DC near zero for mid-gray regions and makes AC coefficients smaller on average, which improves quantization behavior and matches the spirit of the JPEG level shift.

Is this a full JPEG encoder?

No. Real JPEG adds chroma (often subsampled), different quant tables for chrominance, Huffman or arithmetic entropy coding of run-length / category symbols, optional progressive modes, and more. This page isolates the spatial transform + quantization story that creates most of the visible artifacts.

Why does aggressive quantization look blocky?

Each 8×8 block is reconstructed independently from a small set of surviving DCT modes. Neighboring blocks may disagree on edge placement across the shared boundary, so you see a grid of discontinuities — classic blocking artifacts.

What does the zigzag truncation mode represent?

It is a simplified “keep only the lowest spatial frequencies” knob. Real JPEG does not truncate a sharp K in zigzag order without quantization, but the mode matches textbook diagrams that explain energy compaction: early zigzag indices correspond mostly to low horizontal/vertical frequency combinations.

DCT & JPEG Quantization (8×8)

Baseline JPEG-style luminance coding is built from three ingredients on every 8×8 block: (1) subtract 128 from each sample so AC energy is centered; (2) apply a separable 8-point type-II DCT, implemented here with an orthonormal D matrix so inversion is exactly DᵀFD; (3) divide each frequency coefficient by an element of a scaled ISO luminance quantization table, round to an integer, and multiply back — the only lossy step in this toy pipeline. The simulator also offers a second pedagogy mode that skips Huffman coding entirely and simply zeroes trailing coefficients in the canonical JPEG zigzag order after the first K positions, which highlights how low-frequency DCT basis images carry most visible structure while high-frequency bins sharpen edges and fine texture. A 64×64 synthetic grayscale image is processed blockwise; you can click any block to inspect its coefficient heatmaps and a zigzag-ordered trace of the raw DCT before quantization.

Who it's for: Introductory image processing, multimedia, or signals-and-systems students learning why JPEG looks blocky at extreme compression and why chroma subsampling and perceptual weighting matter in full encoders.

Key terms

Discrete cosine transform
JPEG quantization matrix
Zigzag scan
PSNR
8×8 block transform
Lossy compression
Luminance channel

How it works

8×8 type-II DCT on luminance with a −128 level shift (same spirit as baseline JPEG). Choose JPEG quality to scale the standard luminance quantization matrix, or switch to zigzag truncation: keep the first K coefficients in JPEG zigzag order and zero the rest — the staircase you see in textbook AC energy plots. The bottom strip plots zigzag-ordered AC amplitudes for the selected block before any loss (raw DCT).

Key equations

F = D (X−128·1) Dᵀ (8×8)

JPEG: F̂ᵢ = Qᵢ · round(Fᵢ / Qᵢ)

Zigzag: zero F at indices K…63 in scan order

Frequently asked questions

Why subtract 128 before the DCT?: An 8-bit unsigned image lives in [0,255]. Centering around zero (pixel − 128) puts DC near zero for mid-gray regions and makes AC coefficients smaller on average, which improves quantization behavior and matches the spirit of the JPEG level shift.
Is this a full JPEG encoder?: No. Real JPEG adds chroma (often subsampled), different quant tables for chrominance, Huffman or arithmetic entropy coding of run-length / category symbols, optional progressive modes, and more. This page isolates the spatial transform + quantization story that creates most of the visible artifacts.
Why does aggressive quantization look blocky?: Each 8×8 block is reconstructed independently from a small set of surviving DCT modes. Neighboring blocks may disagree on edge placement across the shared boundary, so you see a grid of discontinuities — classic blocking artifacts.
What does the zigzag truncation mode represent?: It is a simplified “keep only the lowest spatial frequencies” knob. Real JPEG does not truncate a sharp K in zigzag order without quantization, but the mode matches textbook diagrams that explain energy compaction: early zigzag indices correspond mostly to low horizontal/vertical frequency combinations.

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DCT & JPEG Quantization (8×8)

How it works

Key equations

Frequently asked questions