of these images were found to be stable and repeatable in all three listening rooms detailed in FIG. 5m, for a broad range of listener head attitudes including directly facing the image, and for a variety of listeners.
We may generalize the placement of narrowband signals, detailed above, in such a manner as to permit broadband signals, representing complicated sources such as speech and music, to be imaged. If the differential amplitudes and phase shifts for the two channels that are derived from a single input signal are specified for all frequencies though the audio band, the complete transfer function is specified. In practice, we need only explicitly specify the differential amplitudes and delays for a number of frequencies in the band of interest. Amplitudes and delays at any intermediate frequency, between those specified, may then be found by interpolation. If the frequencies at which the response is specified are not too widely spaced, and taking into account the smoothness or rate of change of the true response represented, the method of interpolation is not too critical.
In the table of FIG. 15, the amplitudes and delays are applied to the signal in each channel and this is shown generally in FIG. 16 in which a separate sound processor 1500, 1501 is provided. The single channel audio signal is fed in at 1502 and fed to both sound processors 1500, 1501 where the amplitude and phase are adjusted on a frequency dependent basis so that the differential at the left and right channel outputs 1503, 1504, respectively, is the correct amount that was empirically determined, as explained above. The control parameters fed in on line 1505 change the differential phase and amplitude adjustment so that the sound image can be at a different, desired location. For example, in a digital implementation the sound processors could be finite impulse response (FIR) filters whose coefficients are varied by the control parameter signal to provide different effective transfer functions.
The system of FIG. 16 can be simplified, as shown from the following analysis. Firstly, only the difference or differential between the delays of the two channels is of interest. Suppose that the left and right channel delays are t(1) and t(r) respectively. New delays t'(1) and t'(r) are defined by adding any fixed delay t(a), such that:
The result is that the entire effect is heard a time t(a) later, or earlier where t(a) is negative. This general expression holds in the special case where t(a) =-t(r). Substituting:
By this transformation we can always reduce the delay in one channel to zero. In a practical implementation we must be careful to subtract out the smaller delay, so that the need for a negative delay never arises. It may be preferred to avoid this problem by leaving a fixed residual delay in one channel, and changing the delay in the other. If the fixed residual delay is of sufficient magnitude, the variable delay need not be negative.
Secondly, we need not control channel amplitudes independently. It is a common operation in audio engineering to change the amplitudes of signals either by amplification or attenuation. So long as both stereo channels are changed by the same ratio, there is no change in the positional information carried. It is the ratio or differential of amplitudes that is important and must be preserved. So long as this differential is preserved, all of the effects and illusions in this description are entirely independent of the overall sound level of reproduction. Accordingly, by an operation similar to that detailed above for timing or phase control, we may place all of the amplitude control in one channel, leaving the other at a fixed amplitude. Again, it may be convenient to apply a fixed residual attentuation to one channel, so that all required ratios are attainable by attenuation of the other. Full control is then available using a variable attenuator in one channel only.
We may thus specify all the required information by specifying the differential attentuation and delay as functions of frequency for a single ch