Any audio system can be completely measured by impulse response, steady-state frequency response, or selected variations of these, such as square wave, tone burst, or shaped pulse. The measurements will unfortunately alway remain unintelligible to the nontechnical user of audio systems. The difficulty lies not with the user but with the equations and method of test. These do not use the proper coordinates of description for human identification. Heretofore the mathematical validity of Fourier transform methods has inhibited a serious search for alternatives. This paper presents the results of a search which shows that the time domain and frequency domain are only two of an indefinitely large number of valid function space representations for audio-system analysis. A particular function space is presented which uses entities of description that may be related to the human identifiable sound attributes of pitch, spectral distribution, intensity, and temporal or spatial spread of an effective source. A meaningful dialogue may thus be envisioned between the engineer performing objective measurement and the nontechnical listener utilizing subjective terminology. An ortho-normal set of functions is established which allows an expansion of transfer functions of wave propagation (seismic, sonic, electromagnetic) in terms of relative time delay and spectral content of signal. An algorithm is thus established for mapping between time and frequency without the use of a Fourier transform, and characterization of multipath structures may be made indefinitely accurate without the normal limitations of the uncertainty principle. A closed-form solution is made possible for propagation through dispersive absorptive media.
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