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Advanced Applications in Acoustics, Noise and Vibration by Frank Fahy, John Walker

By Frank Fahy, John Walker

Complicated functions in Noise and Vibration offers remedies of acoustic and vibration phenomena including summaries of the newest wisdom, research and strategies at the moment on hand for facing useful difficulties.

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The spectrogam suffers from severe limitations, the most important of which relates to its lack of resolution. At a particular time, the spectrogram corresponds to the magnitude of a windowed Fourier transform; the frequency resolution of this Fourier transform improves as the duration of the window increases. Conversely, the temporal resolution of the spectrogram improves as the window duration reduces. The structure of the spectrogram strongly depends upon the duration of the window employed, and one cannot achieve good time and frequency resolution simultaneously.

Walker (eds) Fundamentals of Noise and Vibration (London, New York: E & FN Spon), pp. 311–372. K. R. (1996) The analysis of nonstationary signals using time frequency methods. Journal of Sound and Vibration, 190, 419–447. Haykin, S. ) (1983) Nonlinear methods of spectral analysis. Vol. 34, Topics in Applied Physics. (Berlin: Springer-Verlag). Hlawatsch, F. and Boudreaux-Bartels, G. (1992) Linear and quadratic time–frequency representations. IEEE Signal Processing Magazine, 21–66. Kaveh, M. R. (1976) An empirical investigation of the properties of the autoregressive spectral estimator.

Iii) Transform this analogue filter into digital form. R. K. 1 Mapping for a unit low-pass filter (all frequencies are expressed in radians) Output filter type Low-pass filter Cut-off frequency High-pass filter Cut-on frequency Band-pass filter Cut-on frequency Cut-off frequency Band-stop filter Cut-off frequency Cut-on frequency Mapping c s→ s c c 0 1 0 1 s→ c s s2 + 0 s→ s 1− s→ s 1− s2 + 0 1 0 0 1 The transformation implemented in step (ii) is relatively simple mapping s→s. 1 details the mappings from a unit low-pass filter to an arbitrary low-pass filter, a high-pass filter and band-pass/band-stop filters.

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