An Improved CZT Algorithm for High-Precision Frequency Estimation

Round 1

Reviewer 1 Report

This paper studies a high-precision frequency estimation based on the improved CZT method. The accurate frequency estimation of exponential sinusoidal is an interesting work in R&D. In general, the manuscript is sound and well presented. However, there are some concerns:

 

The authors state that “the frequencies of multiple superimposed exponentials”, however, the signal model shown in the manuscript is a single tone.

 

Why do the authors select CZT to estimate the frequency? What are the merits of CZT? The authors do not give the reasons in the introduction.

 

The FFT is just a fast implementation of DFT, thus they can not be seen as two algorithms.

 

The explanation of kp is given twice, please correct it.

 

What is the bandwidth of (f1,f2)? Is f2-f1?

 

What is the computational complexity of the proposed CZT?

 

As the parameter q is a key of the proposed method, then how to determine the value of q?

 

In the simulation part, the adopted methods seem to be outdated. Some state-of-art should be compared with the proposed method.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

 

1. Although the title defines that the signal frequency is estimated in noise, nowhere in the paper is it defined which noise is in question - neither in the theoretical discussion, nor in the simulations, nor in the experiment.

2. Based on the experiment and the indicated application, the frequency disturbance is apparently the Doppler effect, which is also not mentioned anywhere in the paper.

3. Experimental and simulation confirmations of the obtained theoretical results are extremely modest due to, it seems to me, very limited performance of the equipment used in the simulations and experiments.

4. The use of orthogonal transformations, because they are of the integral type (integrals), is justified because by integrating, under certain conditions, noise is suppressed. However, different types of noise are suppressed differently.

5. The two most commonly used types of noise in research are Gaussian and uniform noise, so in the theoretical consideration, simulation and experimental verification of the proposed algorithm, it is necessary to investigate at least those two cases.

6. Of particular importance are the resolution and accuracy of the applied AD converter. It is mandatory to mention those parameters of the experiment.

7. Good textbooks, say written by professor Steven Kay, discuss the theoretical Cramer Rao lower bound of the best complete estimation signal in noise and also of frequency as one of signal key parameter.

8. Proposal to the authors:

a. Compare algorithms when the signal is disturbed by Gaussian noise

b. Compare algorithms when the signal is disturbed by uniform noise

c. In both cases, determine how much the estimation error is above the Cramer Rao lower bound

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Appreciate the authors for addressing the comments, as for the state-of-art methods, the following literature should be focused on.

[1]       K. Wang, L. Wang, B. Yan and H. Wen, "Efficient Frequency Estimation Algorithm Based on Chirp-Z Transform," in IEEE Transactions on Signal Processing, vol. 70, pp. 5724-5737, 2022, doi: 10.1109/TSP.2022.3224648.

[2]       H. Wen, C. Li, and L. Tang, "Novel Three-Point Interpolation DFT Method for Frequency Measurement of Sine-Wave," IEEE Transactions on Industrial Informatics, vol. 13, no. 5, pp. 2333-2338, 2017, doi: 10.1109/TII.2017.2681690.

[3]       E. Aboutanios and B. Mulgrew, "Iterative frequency estimation by interpolation on Fourier coefficients," IEEE Transactions on Signal Processing, vol. 53, no. 4, pp. 1237-1242, 2005, doi: 10.1109/TSP.2005.843719.

[4]       Serbes, "Fast and Efficient Sinusoidal Frequency Estimation by Using the DFT Coefficients," IEEE Transactions on Communications, vol. 67, no. 3, pp. 2333-2342, 2019, doi: 10.1109/TCOMM.2018.2886355.

[5]       H. Wen, C. Li and W. Yao, "Power System Frequency Estimation of Sine-Wave Corrupted With Noise by Windowed Three-Point Interpolated DFT," in IEEE Transactions on Smart Grid, vol. 9, no. 5, pp. 5163-5172, Sept. 2018, doi: 10.1109/TSG.2017.2682098.

 

[6]       E. Aboutanios, “Generalised DFT-based estimators of the frequency of a complex exponential in noise,” in Proc. 3rd Int. Congr. Image Signal Process., Yantai, China, Oct. 2010, pp. 2998–3002.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

Comment
1. In Fig. 2. highlight better the graph of the proposed algorithm - so that it is at least as noticeable as the CZT algorithm graph.

A proposal for possible future research
1. Consider the application of window function banks.

Author Response

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Author Response File: Author Response.pdf