Structural Dynamics and Vibration in Practice

9

Fourier Transformation and Related Topics

Contents

9.1 The Fourier series and its developments

9.2 The discrete Fourier transform

9.3 Aliasing

9.4 Response of systems to periodic vibration

References

In this chapter, we introduce some of the basic tools that will be required for the practical analysis of vibration data, preparatory to the discussion of random vibration in Chapter 10. The classical Fourier series is first introduced, looking briefly at how the Fourier integral and the Fourier transform are related to it. We then consider the discrete Fourier transform, or DFT, the ‘computer-friendly’ version of the Fourier series, and the basis of most modern digital vibration analysis. The use of digital signal processing brings with it ...