annel. A fixed, frequency-independent attentuation and delay may be specified for the second channel; if these are left unspecified, we assume unity gain and zero delay.
Thus, for any one sound image position, and therefore any one left/right transfer function, the differential phase and amplitude adjusting (filtering) may be organized all in one channel or the other or any combination in between. One of sound processors 1500, 1501 can be simplified to no more than a variable impedance or to just a straight wire. It can not be an open circuit. Assuming that the phase and amplitude adjusting is performed in only one channel to provide the necessary differential between the two channels the transfer functions would then be represented as in FIGS. 17A and 17B.
FIGS. 17A represents a typical transfer function for the differential phase of the two channels, wherein the left channel is unaltered and the right channel undergoes phase adjustment on a frequency dependent basis over the audio spectrum. Similarly, FIG. 17B represents generally a typical transfer function for the differential amplitude of the two channels, wherein the amplitude of the left channel is unaltered and the right channel undergoes attentuation on a frequency dependent basis over the audio spectrum.
It is appreciated that the sound positioners: 1500, 1501 of FIG. 16, for example, can be analog or digital and may include some or all of the following circuit elements: filters, delays, inventors, summers, amplifiers, and phase shifters. These functional circuit elements can be organized in any fashion that results in the transfer function.
Several equivalent representations of this information are possible, and are commonly used in related arts.
For example, the delay may be specified as a phase change at any given frequency, using the equivalences:
Caution in applying this equivalence is required, because it is not sufficient to specify the principal value of phase; the full phase is required if the above equivalences are to hold.
A convenient representation commonly used in electronic engineering is the complex s-plane representation. All filter characteristics realizable using real analog components (any many that are not) may be specified as a ratio of two polynomials in the Laplace complex frequency variable s. The general form is: ##EQU1##
Where T(s) is the transfer function in the s plane, Ein(s) and Eout(s) are the input and output signals respectively as functions of s, and the numerator and denominator functions N(s) and D(s) are of the form:
N(s)=a.sub.o +a.sub.1 s+a.sub.2 s.sup.2 +a.sub.3 s.sup.3 +. . . +a.sub.n s.sup.n (6)
N(s)=b.sub.o +b.sub.1 s+b.sub.2 s.sup.2 +b.sub.3 s.sup.3 +. . . +b.sub.n s.sup.n (7)
The attraction of this notation is that it may be very compact. To specify the function completely at all frequencies, without need of interpolation, we need only specify the n+1 coefficients a and the n+1 coefficients b. With these coefficients specified, the amplitude and phase of the transfer function at any frequency may readily be derived using well-known methods. A further attraction of this notation is that it is the form most readily derived from analysis of an analog circuit, and therefore, stands as the most natural, compact, and well-accepted method of specifying the transfer function of such a circuit.
Yet another representation convenient for use in describing the present invention is the z-plane representation. In the preferred embodiment of the present invention, the signal processor will be implemented as digital filters in order to obtain the advantage of flexibility. Since each image position may be defined by a transfer function, we need a form of filter in which the transfer function may be readily and rapidly realized with a minimum of restrictions as to which functions may be achieved. A fully programmable digital filter is appropriate to meet this requirement.
Such a digital filter may operate in the frequency domain, in which case, the signal is first Fourier transformed to move it from a time domain representation to a 