ABSTRACT
The mathematical basis for spectrum analysis is the Fourier integral, which was provided by the mathematician Joseph Fourier in the early 1800s, long before modern rotating machinery. However, in modern times prior to the FFT algorithm, which utilizes modern digital computational methods, the transform of a measured time-base signal into the frequency domain required costly “off-line” processing with slow turnaround. Specificially, a taped recording of the analog signal was processed through several narrow-bandwidth analog filters (Sec. 4 in Chapter 7) with center-band frequencies spanning the relevant frequency range. Pre-FFT spectrum analyzers were cumbersome pieces of electronic equipment to operate successfully, requiring a technician experienced in how to tune and adjust the bandwidth filters to achieve optimum results for a given time-base signal record. Understandably, pre-FFT spectrum analysis was very sparingly used. The mathematical details of Fourier series, Fourier integrals, and FFTs are now standard parts of the mathematics component in college engineering curricula and are well covered in numerous mathematical and engineering analysis textbooks and
covered here. Instead, a more heuristic explanation of spectrum analysis is given here to aid the machinery vibration practitioner in understanding the direct connection between a time-base signal and its frequency spectrum.
