Sinusoidal Frequency Estimation based on the Time Derivative of the STFT Phase Response

This paper presents the phase derivative FFT (PDFFT)-a computationally efficient algorithm for estimating the frequency of a sinusoid from the short time Fourier transform (STFT). Upon obtaining initial coarse estimates from the FFT of a given frame, the PDFFT makes further refinement to the frequency estimate using only the time derivative of the phase response. The algorithm is derived and is shown to require only 4 multiplies per peak. Single frequencies in the presence of noise are resolved well, outperforming the commonly used quadratically interpolated FFT (QIFFT) method even with zero-padding. The algorithm is then used to separate two sinusoids of close frequency proximity that appear as a single peak in the magnitude spectrum