Short-time power spectra: Estimation and acoustical applications

Tapio Lahti

Research output: Book/ReportReport

Abstract

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.
Original languageEnglish
Place of PublicationEspoo
PublisherVTT Technical Research Centre of Finland
Number of pages168
ISBN (Print)951-38-1827-6
Publication statusPublished - 1983
MoE publication typeD4 Published development or research report or study

Publication series

SeriesValtion teknillinen tutkimuskeskus. Tutkimuksia - Research Reports
Number209
ISSN0358-5077

Fingerprint

fast Fourier transformations
power spectra
frequency response
silencers
time signals
acoustics
acoustic impedance
transmission loss
loudspeakers
background noise
absorbents
sound fields
ducts
ambiguity
rooms
signal processing
absorptivity
slabs
impedance
radiation

Keywords

  • power spectra
  • frequencies
  • acoustics
  • absorptivity

Cite this

Lahti, T. (1983). Short-time power spectra: Estimation and acoustical applications. Espoo: VTT Technical Research Centre of Finland. Valtion teknillinen tutkimuskeskus. Tutkimuksia - Research Reports, No. 209
Lahti, Tapio. / Short-time power spectra : Estimation and acoustical applications. Espoo : VTT Technical Research Centre of Finland, 1983. 168 p. (Valtion teknillinen tutkimuskeskus. Tutkimuksia - Research Reports; No. 209).
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Lahti, T 1983, Short-time power spectra: Estimation and acoustical applications. Valtion teknillinen tutkimuskeskus. Tutkimuksia - Research Reports, no. 209, VTT Technical Research Centre of Finland, Espoo.

Short-time power spectra : Estimation and acoustical applications. / Lahti, Tapio.

Espoo : VTT Technical Research Centre of Finland, 1983. 168 p. (Valtion teknillinen tutkimuskeskus. Tutkimuksia - Research Reports; No. 209).

Research output: Book/ReportReport

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N2 - 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.

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Lahti T. Short-time power spectra: Estimation and acoustical applications. Espoo: VTT Technical Research Centre of Finland, 1983. 168 p. (Valtion teknillinen tutkimuskeskus. Tutkimuksia - Research Reports; No. 209).