Measurement of distortion product phase in the ear canal of the cat

Amplitudes of odd order distortion products (DPs) that are detected in animal ear canals have been used to probe cochlear health, to search for cochlear amplification, and to measure aspects of cochlear mechanical frequency response. Like the DP amplitude, DP phase is also an important measure of the cochlear mechanical response. Reported here are measurements of DP phase in the ear canal of the cat. The phase data show frequency-dependent time delays. One of these delays is a function of $f_2,$ the frequency of the higher-frequency primary. Hence the DP phase ${\phi }_d$ is of the form ${\phi }_d{\mathrm{=\phi }}_0{\mathrm{+\omega }}_d\mathrm{\tau ,}$ where ${\omega }_d$ is the DP angular frequency and τ is a fixed time delay. Our results show that ${\phi }_d$ is independent of input level $a_2$ as long as the ratio $a_2{\mathrm{/a}}_1\text{⩽2,}$ where $a_2$ and $a_1$ are the amplitudes of the input tones. As $a_2{\mathrm{/a}}_1$ becomes greater than two, the fixed time delays increase for DPs whose frequencies are less than the frequencies of the input tones. When both levels are varied together the delay increases as the levels decrease. There can be phase changes as large as π associated with deep nulls in the DP magnitude for the two lower-frequency DPs. Features of the nulls may be modeled assuming that there is partial reflection of the DP wave from the DP place. The assumption of energy reemitted from the DP place also explains amplitude-ratio-dependent time delays and 2π level-dependent bifurcations in phase. The DP phase shows different dependencies for $f_2\text{<1\hspace{0.17em}}\mathrm{kHz}$ compared to $f_2\text{>2\hspace{0.17em}}\mathrm{kHz}.$