Performance comparison of four DFT interpolation techniques for accurate fundamental frequency analysis of harmonic signals

Hee-Suk Pang

doi:10.7776/ASK.2026.45.3.323

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2026 Vol.45, Issue 3 Preview Page

Performance comparison of four DFT interpolation techniques for accurate fundamental frequency analysis of harmonic signals 배음 신호의 정밀한 기본주파수 분석을 위한 네 가지 DFT 보간 기법의 성능 비교

31 May 2026. pp. 323-331

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Abstract

When analyzing the fundamental frequency of a harmonic signal based on the Discrete Fourier Transform (DFT), a fine frequency estimation method should be applied to minimize the estimation error. For this purpose, we qualitatively analyzed the characteristics of the estimation errors for DFT interpolation techniques such as Quadratic Fit (QF), Interpolated Fast Fourier Transform (IFFT), Weighted Multipoint Interpolated DFT (WMIDFT), and Corrected Quadratically Interpolated FFT (CQIFFT), and compared the performance of each method using simulation experiments and recorded flute sound. The results showed that the optimal method varied depending on the fundamental frequency, Signal to Noise Ratio (SNR), and number of harmonics. CQIFFT required an additional computational load compared to the other techniques, but performed well either at low SNR or when the SNR is high and the influence of harmonics was weak, such as when the fundamental frequency was high or the signal consisted of a single sinusoid. WMIDFT was effective when the fundamental frequency was low at high SNR, and IFFT outperformed WMIDFT at low SNR. The results are expected to be helpful in selecting a DFT interpolation technique for fundamental frequency estimation.

Keywords

Fundamental frequency

Harmonic signal

Discrete Fourier Transform (DFT)

Interpolation techniques

Signal to Noise Ratio (SNR)

배음 신호의 기본주파수를 이산 푸리에 변환(Discrete Fourier Transform, DFT)에 기반해서 분석할 경우, 추정 에러를 최소화하기 위해서 정밀한 주파수 추정 방법을 사용해야 한다. 이를 위해서 DFT 보간 기법인 2차 피팅(Quadratic Fit, QF), Interpolated Fast Fourier Transform(IFFT), Weighted Multipoint Interpolated DFT(WMIDFT), Corrected Quadratically Interpolated FFT(CQIFFT)에 대해 주파수 추정 에러의 특성을 정성적으로 분석하고, 모의 실험 및 녹음된 플루트음을 이용해 각 보간 기법의 성능을 비교하였다. 그 결과 각 보간 기법들은 기본주파수, 신호대잡음비(Signal to Noise Ratio, SNR), 배음의 수 등에 따라서 최적의 방법이 달라지는 것으로 나타났다. CQIFFT는 다른 방법들에 비해 연산량이 더 많으며, 신호대잡음비가 낮은 경우 혹은 신호대잡음비가 높고 기본주파수가 상대적으로 높거나 단일 정현파로 구성되는 등 배음의 영향이 작은 경우 성능이 좋았다. WMIDFT는 신호대잡음비가 높고 기본주파수가 낮은 경우 성능이 좋았으며, IFFT는 신호대잡음비가 낮은 경우 WMIDFT보다 좋은 성능을 보였다. 이상의 결과는 배음 신호의 기본주파수를 추정하기 위해 DFT 보간 기법을 선택하는 데 도움이 될 것으로 기대한다.

키워드

배음 신호

기본주파수

이산 푸리에 변환(Discrete Fourier Transform, DFT)

보간 기법

신호대잡음비(Signal to Noise Ratio, SNR)

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Information

Publisher :The Acoustical Society of Korea
Publisher(Ko) :한국음향학회
Journal Title :The Journal of the Acoustical Society of Korea
Journal Title(Ko) :한국음향학회지
Volume : 45
No :3
Pages :323-331
Received Date : 2026-03-09
Accepted Date : 2026-04-20
DOI :https://doi.org/10.7776/ASK.2026.45.3.323

The Journal of the Acoustical Society of KoreaISSN:1225-4428(Print) 2287-3775(Online)한국음향학회

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