By J. M. Montalvão E Silva (auth.), Júlio M. M. Silva, Nuno M. M. Maia (eds.)

ISBN-10: 0792358945

ISBN-13: 9780792358947

ISBN-10: 9401145032

ISBN-13: 9789401145039

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M. , Silva, J. M. M. , England. McConnell, K. G. (1995), Vibration Testing: Theory And Practice, Wiley Interscience. Inman, D. J. A. , Lammens, S. and Sas, P. (1998), Modal Analysis Theory and Testing, KU Leuven, Belgium. INTRODUCTION TO SIGNAL PROCESSING Part I: Fundamentals ofSignal Processing J. K. HAMMOND Institute of Sound and Vibration Research University of Southampton 1. Introduction Signal processing is the science of applying transformations to measurements, to facilitate their use by an observer or a computer and the analysis of data involves the three phases of data acquisition, processing and interpretation.

The Fourier transform of the product of two time functions is the convolution of their transforms. For the particular case of the 'rectangular' data window above, W(f) = Tsin(nIT) (nIT) and through the convolution operation this widens and distorts the 'true' Fourier transform X(t). This distortion is sometimes called smearing (due to the main lobe) and 'leakage' since components of X(t) at values other than g = f 'leak' through the side lobes to contribute to the value of XT at f. For example, suppose x(t) = 2npt, then 1 X(f) =2 [O(f + p) + O(f - p)] and so 1 XT(f) =2 [W(f + p) + W(f - p)] showing that the shape of the spectral window (in the frequency domain) replaces the delta function.

M. , Silva, J. M. M. , England. McConnell, K. G. (1995), Vibration Testing: Theory And Practice, Wiley Interscience. Inman, D. J. A. , Lammens, S. and Sas, P. (1998), Modal Analysis Theory and Testing, KU Leuven, Belgium. INTRODUCTION TO SIGNAL PROCESSING Part I: Fundamentals ofSignal Processing J. K. HAMMOND Institute of Sound and Vibration Research University of Southampton 1. Introduction Signal processing is the science of applying transformations to measurements, to facilitate their use by an observer or a computer and the analysis of data involves the three phases of data acquisition, processing and interpretation.

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