The direct simulation of impulse responses using the time domain formulation of the BEM is still not recommended due to stability problems in the solutions. The method undertaken and described below is based on using the Inverse Fourier transforms of the computed responses in the frequency domain.
It is possible to visualise the propagation of the spherical wave, impinging on the surface of the head, by calculating the inverse Fourier transform of the frequency response at each field point. To ensure causality of the impulse response of each point, and also for the clarity of animation, the response was multiplied with a half Hanning window with the Nyquist frequency being at 6.4 kHz. The following steps were followed:

• The frequency response of each field point around KEMAR is calculated with the DBEM around the head up to 6.4 kHz.

• The frequency is 'mirrored' at the Nyquist frequency by appending the conjugate values.

• The new frequency response is multiplied by half of the required window in the frequency domain.

• An inverse FFT is applied followed by a cyclic shift to produce a delay at half the number of the sampling points.

When the spherical wave impinges on the head, a secondary wave is seen to propagate backwards. When the main wave leaves the head, another spherical wave appears. The amplitude of this wave is small, compared with the incident wave, and its effect was emphasised in this simulation by positioning the source in the near field at 0.5 m away. The further away the source, the less significant this effect.