One objective way to evaluate the effect of noise reduction algorithms in hearing aids is to measure the increase in signal-to-noise-ratio (SNR). To this end, Hagerman and Olofsson presented a method where multiple recordings take place and the phase of one signal is inverted between the measurements. This phase inversion method allows one to separate signal and noise at the output of the hearing aid so that the increase in SNR can be evaluated. However, only two signals can be distinguished, for example, speech and noise. As many realistic situations include more than two signals, we extend the method to an arbitrary number of signals. Two different approaches are discussed. For the first one, groups of the signals are created and presented in such a way that the basic phase inversion method can be used. The second, more efficient approach defines a linear system of equations considering all signals. As the robustness of this approach depends on the structure of the system matrix, the design of this matrix is described in detail. To prove the concept, the proposed efficient method was applied to a setup in which nine different signals were presented by eight loudspeakers, and an analysis of errors was performed. With this setup, a state-of-the-art hearing aid was analyzed for four different settings, that is, with the digital noise reduction or the directional microphones turned on or off. As a result, the SNRs for all directions can be investigated individually.

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The phase inversion method, a technical measurement procedure, is often used to evaluate the performance of noise reduction algorithms in hearing aids. However, a detailed comparison of these technical measurements with the perceived loudness is missing. Therefore, commercially available hearing aids of six different manufacturers were evaluated technically and in a study with 18 normal-hearing listeners. First, the output signals of the hearing aids with and without activated noise reduction were recorded in a test box. Then, the test subjects evaluated the perceived loudness of these recordings within multiple two alternative forced choice (2-AFC) tasks. During one task, the test subjects had to focus either on the speech or noise signal and were asked to select the louder of two signals, which both contained a mixture of speech and noise. These results provide not only the perceived SNR but also the perceived speech and noise levels. Comparing the results of the 2-AFC tasks and the phase inversion method basically shows good agreement. Nevertheless, a simple computation of the sound pressure level can lead to significant deviations. Therefore, another possibility for the analysis of the results of the phase inversion method to better match the perceived loudness is presented.