On Performance of Sparse Fast Fourier Transform Algorithms Using the Aliasing Filter

Round 1

Reviewer 1 Report

The paper is a study of performances of Sparse Fast Fourier Transform  using the aliasing filter.

But what are the original elements? What is the novelty of the paper?

Thus, the contribution is marginal and it lacks of sufficient novelty.

All the equations and theorems  are proposed by authors? If not, it should be cited some references. The state-of-the art is very summary described.

What is the meaning of the parameters from figure 1?

There are some methods used in this study and they should be a little bit described, not just given the reference (for example Matrix Pencil Method).

On page 19, it is the total runtime complexity of DSFFT. Based on what? Where did this expression come from?

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

The paper analyze six typical algorithms using the aliasing filter. Two categories of experiments, for computing the signals by a standard testing platform both in the exactly sparse case and general sparse case, was made. 

Comments:

Citation of sources is sparing and occurs practically only in the introduction, omitting the reference to the source when describing the algorithms.

The form used in the article is strange, with references to equations before they appear, e.g. equations (7), (8) (9) and others

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

In this manuscript, the authors reported the performance of sparse Fast Fourier transform algorithm using the aliasing filter. Discrete FFT and FFT are widely used techniques for signal processing and spectrum analysis.

I recommend accepting this paper after addressing following comments.

General comments

The paper is long and descriptive. This will be helpful for readers outside the signal processing community also to get a solid idea about FFT and SFFT algorithms. But I think the writing style and English need to be improved before publishing the manuscript. Also, check all the citation properly. In many places in manuscript, there are no proper citation numbers near sentences stating previous works/principles. A few are listed in the comments below too.

Comments:

Line 19: Rephrase the sentence “which can compute a signal of size N in O(NlogN) time and use O(N) samples” for better readability. Add citation at the end of this sentence [journal].

Line 62: What do you mean by “sampling interval less than 1”. It generates confusion. Which unit are you speaking?

Line 77: “The algorithms using the flat filter are probabilistic algorithms with spectrum leakage” add a citation number for reference. I do not think it is a general statement.

The sentences below Fig 1, Fig. 2 and Fig.3 have no line numbers, why?

Line 125:  add citation/reference number for the sentence on “Bose-Chaudhuri-Hocquenghem(BCH)”

In figure 1 and Fig. 2 letters of legends are touching on the block diagram lines. It needs to be corrected for better aesthetic. For example: The “e” of single-ton is overlapping with the vertical line in Fig.2

Figure 4-6 caption can be more descriptive like the Fig.3 one.

Also, it would be nice to add a long caption for Fig.7-Fig.12. Because they are showing the comparison of different algorithms. So, descriptive Figure caption will be helpful for readers to get the essence of the paper quickly even though it is explaining in the text.

In the results section you have not explained how the usage of aliasing filter will prevent the spectrum leakage in comparison with a flat filter. I think this advantage needs to be explained in detail.

In conclusion, I think it would be nice to add a few applications of your algorithms or which applications has maximum benefits if you employ SFFT with aliasing filter.

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Not all the answers from author's reply can be found in the paper.

The contributions should be clearly highlighted. Also, the original elements, the novelty of the paper...all of these should be found in the final paper.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf