A Fine-Resolution Frequency Estimator in the Odd-DFT Domain

• Published in: IEEE signal processing letters Vol. 22; no. 12; pp. 2489 - 2493
• Main Authors: Dun, Yujie, Liu, Guizhong
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.12.2015; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Audio processing; Conversion; Digital broadcasting; Discrete Fourier transforms; Estimators; Exact solutions; Filter banks; Frequency estimation; Frequency-domain analysis; Mathematical analysis; MDCT; Noise; odd-DFT; Signal processing; Signal processing algorithms; Speech
• ISSN: 1070-9908; 1558-2361
• DOI: 10.1109/LSP.2015.2496276

Although many frequency estimation methods are available, few are designed for high-quality speech and audio processing systems, which typically use the modified discrete cosine transform (MDCT) as their analysis filter bank. In this letter, we propose a low complexity frequency estimator that is suitable for MDCT-based systems and that operates in the odd-DFT domain. Taking a complex exponential in noise as the input and deriving the analytical expression of its odd-DFT coefficient, we obtain an interpolated odd-DFT-based frequency estimator. Experiments show that the proposed estimator outperforms all other reported odd-DFT/MDCT domain estimators and has precision that is similar to that of representative DFT domain frequency estimators. The overhead for incorporating this estimator into a speech and audio processing system is small due to the simple odd-DFT to MDCT conversion. The corresponding magnitude and phase estimators are also proposed in this letter.