The analysis of many actual engineering problems can be greatly enhanced through the application of fast Fourier transform (FFT) signal processing. The purpose of this paper is to demonstrate some typical problem solving approaches and subsequent solutions obtainable through FFT analysis. The problems and solution techniques are chosen to illustrate the use of the various available spectral quantities. The topics discussed include: (1) source identification and preventative maintenance monitoring through comparison of power spectra; (2) the estimation of radiated acoustic intensity using the cross spectrum between two closely spaced microphones; (3) machinery noise source identification via the ordinary coherence function; and (4) the measurement and estimation of dynamic structural characteristics from frequency response functions. Techniques to assess the spectral quality for each application are discussed to ensure that accurate results are obtained. Each topic area is presented in a pragmatic fashion to illustrate the use and interpretation of the spectra required for each application.