The Journal of the Acoustical Society of Korea (한국음향학회지)

The Acoustical Society of Korea (한국음향학회)
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A Study on performance comparison of frequency estimators for sinusoid

정현파 신호 주파수 추정 알고리즘의 추정 정확도 비교 연구

  • Cho, Hyunjin (Department of Electrical Engineering, Republic of Korea Naval Academy)
  • Received : 2018.04.02
  • Accepted : 2018.11.29
  • Published : 2018.11.30
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Abstract

This paper presents performance comparison of several high-resolution frequency estimation algorithms for pure real tone signal. Algorithms are DFT (Discrete Fourier Transform - for reference purpose), Jacobsen, Candan, reassignment and Cedron. Each algorithm is evaluated under various experimental conditions, e.g., different SNR (Signal to Noise Ratio), window function and window length and performance is compared in the perspective of bias, MSE (Mean Square-Error) and variance. Experimental results indicate that Cedron algorithms works well in the most cases. For actual usage in the engineering problem, each algorithm needs additional analysis and modification.

본 논문은 정현파 신호에 대해 고해상도 주파수 추정이 가능한 알고리즘들의 성능을 비교 분석하였다. 비교 대상 알고리즘은 총 5가지로 DFT(Discrete Fourier Transform - 성능 평가 기준), Jacobsen, Candan, 재할당(Reassignment) 알고리즘 및 Cedron 알고리즘이다. 각 알고리즘의 성능을 SNR(Signal to Noise Ratio), 윈도우 함수, 윈도우 길이 등의 요소를 변화시켜가며 성능을 측정하였다. 알고리즘의 성능 평가는 편의 및 오차(Mean Square Error, MSE), 분산을 이용하여 측정하였으며, 실험결과 Cedron 알고리즘이 좋은 성능을 보였다. 실제 공학문제에서의 활용을 위해서는 각 알고리즘별로 보다 다양한 조건에서 실험 결과를 분석하고 개선시킬 필요가 있다.

Keywords

GOHHBH_2018_v37n6_457_f0001.png 이미지

Fig. 1. Frequency leakage phenomenon. True normalized frequency is 0.2. Two different NFFT (fft lengths) cause different results (Normalized frequency should be multiple of 1/N for preventing leakage).

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Fig. 2. Comparison of various window function effects on the test signal: (a) frequency range 100 Hz ~ 800 Hz (b) enlarge 250 Hz ~ 400 Hz.

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Fig. 3. Frequency estimation performance under noise-free environment with specific window functions: (a) rectangular window, (b) hamming window (c) hanning window (d) blackman window.

GOHHBH_2018_v37n6_457_f0004.png 이미지

Fig. 4. Performance of various frequency estimation algorithms with specific window functions (a) rectangular window, (b) hamming window (c) hanning window (d) blackman window.

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Fig. 5. Performance of various frequency estimation algorithms with various window functions.

Table 1. Selected MSE result at 6 dB SNR with 256 NFFT.

GOHHBH_2018_v37n6_457_t0001.png 이미지

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