Avoiding spectral leakage in measurements of distortion-product otoacoustic emissions

The typical measurement of distortion-product otoacoustic emissions (DPOAEs) relies on the discrete Fourier transformation (DFT) to extract amplitude and phase of the response at the 2f1-f2 DPOAE frequency, f1 and f2 being the frequencies of the stimulus. The DFT measures the DPOAE response accurately, not when the DPOAE frequency is exactly at a DFT bin, but when the DPOAE frequency and both stimulus frequencies are at a DFT bin. The stimulus frequencies are typically varied so that the ratio f2/f1 is constant, and this strategy is not readily compatible with the fixed spacing between frequency bins of the DFT. This study shows that there is not a one-to-one relation between DFT resolution and DPOAE resolution. Ratios of 6/5 (1.20), 11/9 (1.222...) and 5/4 (1.25) are the only ones near the well-studied 1.22, where the DPOAE frequency and both stimulus frequencies are at a DFT bin. They allow for a maximum DPOAE resolution of 4, 7 and 3 DFT bins, respectively. Simulation shows that, as the distortion-frequency 2f1-f2 decreases, the error at 2f1-f2 due to spectral leakage from f1 and f2 increases to more than 10 dB depending on relative levels. Controlling for this error by selecting “good” ratios therefore allows DPOAE measurements at low frequencies. Eighteen normal-hearing human subjects had DPOAE levels measured as a function of f2/f1. 2f1-f2 was kept around 246 and 1231 Hz, but DPOAEs were also measurable at 123 Hz. The ratio giving the maximum DPOAE level increases as the distortion-frequency decreases. Contrary to the impression one might get from the literature, there is no indication that the nonlinearity producing distortion in the cochlea rolls off towards low frequencies.