Short-time power spectra: Estimation and acoustical applications

The study deals with the theoretical background and practical acoustical applications of the short-time FFT frequency analysis. The fundamental concept of the instantaneous spectrum is reviewed. Its practical estimation by the lagged window FFT and the straightforward extension to two-channel signals and cross-spectra are presented. The inherent limitations of the short-time approach on the estimation of frequency response and the identification of distributed acoustical systems are discussed. Several examples of application in central areas of technical acoustics are given. The specific acoustic impedance is shown to be determinable directly in any acoustical environment, as a function of spatial position and (assuming local reaction) using any sound field present. The direct measurement of impedance is extended to give directly the radiation efficiency, the absorption coefficient, the incident sound power, and the transmission loss. The tested examples include an absorbent, a window, a floor slab excited by impact noise, and a silencer in a duct. The frequency response of a loudspeaker is determined in an ordinary room. Background noise outdoors is shown to be suppressed by a delay in short-time dual FFTs. A collection of more advanced short-time signal processing by the FFTs involves the group delay, an analytic (complex) signal by Filbert transform, the instantaneous frequency, the complex instantaneous spectrum and the ambiguity function.