Recursive algorithm, architectures and FPGA implementation of the two-dimensional discrete cosine transform
Bibliographic record
Abstract
A new recursive algorithm and two types of circuit architectures are presented for the computation of the two-dimensional discrete cosine transform (2D DCT). The new algorithm permits to compute the 2D DCT by a simple procedure of the 1D recursive calculations involving only cosine coefficients. The recursive kernel for the proposed algorithm contains a small number of operations. Also, it requires a smaller number of pre-computed data compared with many of existing algorithms in the same category. The kernel can be easily implemented in a simple circuit block with a short critical delay path. In order to evaluate the performance improvement resulting from the new algorithm, an architecture for the 2D DCT designed by direct mapping from the computation structure of the proposed algorithm has been implemented in an FPGA board. The results show that the reduction of the hardware consumption can easily reach 25% and the clock frequency can increase 17% compared with a system implementing a recently reported 2D DCT recursive algorithm. For a further reduction of the hardware, another architecture has been proposed for the same 2D DCT computation. Using one recursive computation block to perform different functions, this architecture needs only approximately one-half of the hardware that is required in the first architecture, which has been confirmed by an FPGA implementation.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".