Jean Baptiste Joseph Fourier (1768 - 1830) was a French Mathematician best known for initiating the investigation of the Fourier Series, and their applications to problems of heat transfer and vibrations. Since Fourier's time, numerous papers and books dealing with Fourier Theory have been published. The Discrete Fourier Transform (DFT) is a discrete approximation of the Fourier Integral, and is used to transform time series data from the time domain to the frequency domain. The DFT is cumbersome when working with large sets of data, so in the 1960's, J.W. Tukey and J.W. Cooley developed the Cooley - Tuckey algorithm, also known as the Fast Fourier Transform (FFT), which quickly and efficiently evaluates the DFT.
The plots below show the Frequency, Amplitude, and Power spectrums of an automobile's vibration data. A total of 4096 data points were analyzed at a sampling rate of 10khz.
ANALYSIS OF CAR ENGINE'S VIBRATION DATA
Motors, pumps, compressors, rollers, and other rotating machinery vibrate when they are in operation. When a machine vibrates too much, it becomes obvious that something is wrong. The best approach to maintaining rotating machinery is to take periodic readings from acceleration transducers. Imbalances, misalignments, and bearing instabilities will appear as changes in the machine's vibration (power) spectrum, or 'Mechanical Signature'. Corrective action can then be taken before a worsening situation becomes critical.