Review Reports

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This paper researches a fast DCT-VIII algorithms for short-length input sequences, the author has done some work, but there are still some issues in the paper that need to be revised, the specific problems are as follows:

(1) The abstract is too long and fails to condense the methods and measures studied well. It is suggested to optimize the abstract.

(2) The contribution described in the paper is merely a simple explanation in part 1. There is no indication that the author has distilled innovative research methods and made significant contributions.

(3) In part 3, the author deduced the specific algorithm of the research, and the train of thought was relatively clear. However, there were no specific verification methods or results, which raised doubts about the feasibility of the entire algorithm.

(4) In part 4, the verification idea provided by the author is quite simple. How do the results of this part prove that the fast DCT-VIII algorithms for short-length input sequences in the study are correct? In addition, compared with other existing methods, what are the specific advantages of the studied algorithm? Which practical problems have been solved?

(5) Although this paper provides some research methods, the logical relationships among the key contents of the research methods are not very clear. It is suggested that the author carefully sort out the research algorithms and reflect the highlights of the studied algorithms.

Comments on the Quality of English Language

The language expression of the paper is acceptable

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The manuscript “Fast DCT-VIII Algorithms for Short-Length Input Sequences” addresses an important and specialized topic in digital signal processing, namely the efficient computation of short-length DCT-VIII transforms. The paper is technically sound, well-motivated by applications in image/video coding, and contributes new structural factorizations for input lengths 3-7. The work is relevant to both theoretical DSP research and practical codec design. The structural approach is well-justified, and the choice of input lengths (3-7) is appropriate for demonstrating the method’s applicability.

Some recommendations for improving the manuscript:

The introduction provides a broad overview of DCT applications and situates DCT-VIII within the VVC standard. However, some references are dated or unevenly distributed. For example, more recent codec-related studies could be cited to strengthen the context. The motivation for focusing on short-length transforms could be emphasized more clearly.

The derivations are mathematically correct but sometimes dense. Certain steps (e.g., permutations, sign alterations, decomposition into submatrices) could benefit from clearer explanations or illustrative examples. The notation is heavy; a summary table of symbols would help readability.

The results are presented with explicit factorizations and data flow graphs. The comparison of arithmetic complexity is convincing, though the increase in additions should be discussed more thoroughly in terms of practical trade-offs.

The conclusions are supported by the results, highlighting both the reduction in multiplications and the modularity of the algorithms. However, the potential impact on hardware implementation could be elaborated.

The data flow graphs are useful but somewhat schematic. Adding captions that explain the computational meaning of each node would improve clarity. No comparative table of operation counts across different algorithms is provided; such a table would strengthen the results section.

In conclusion:

Please, strengthen the introduction by clarifying why short-length DCT-VIII transforms are particularly important in modern codecs and by citing more recent VVC-related studies.

Please, improve clarity of derivations: provide intermediate steps or illustrative examples for permutations and matrix decompositions. A notation summary table would be very helpful.

Please, discuss trade-offs: while multiplications are reduced, additions increase. Explain how this affects practical implementations (e.g., hardware vs. software).

Please, enhance captions of data flow graphs to explain computational meaning; consider adding a comparative table of operation counts.

Please, correct minor errors and streamline long sentences.

Please, expand on implications for hardware/software implementations and possible extensions to larger block sizes.

 

Comments on the Quality of English Language

English could be improved. The manuscript is understandable but contains awkward phrasing and occasional grammatical issues. For example, “arize” should be “arise,” and some sentences are overly long. Careful language editing is recommended.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

（1）Although the current revised manuscript has undergone some modifications, it still lacks sufficient verification of the algorithm and lacks strong persuasiveness. It is suggested that a more reasonable comparative verification of the studied algorithm be provided, along with more objective results.

（2）In the discussion section, it is suggested that the author describe the advantages and limitations of the current research methods, and at the same time present future research developments to enhance the readability of the paper.

（3）It is suggested that the author use fonts of other colors to highlight the revised content when revising the manuscript.

Comments on the Quality of English Language

The language expression of the paper is acceptable

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 3

Reviewer 1 Report

Comments and Suggestions for Authors

The current revised manuscript has answered the questions raised. There are no other questions at present.

Comments on the Quality of English Language

The language expression of the paper is acceptable