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

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.