Introduction to Fast Fourier Transform (FFT) Analysis

Vibration data is recorded as a function of time, meaning the change in some value, such as acceleration, over time. After recording, it is often advantageous to transform the data into a different domain for analysis. Patterns not apparent in the time domain are visible in others, giving engineers a clearer understanding of their product’s vibrational behavior.

Fast Fourier Transform

Engineers often analyze vibration as a function of frequency. The fast Fourier transform (FFT) is a computational tool that transforms time-domain data into the frequency domain by deconstructing the signal into its individual parts: sine and cosine waves. This computation allows engineers to observe the signal’s frequency components rather than the sum of those components.

The FFT helps engineers determine the excitation frequencies in a complex signal and their amplitude. It also highlights changes in frequency and amplitude and harmonic excitation in the selected frequency range.

For a complex signal, the FFT can help to answer:

  • What frequencies are being excited?
  • What is the amplitude at each frequency?
  • What changes throughout the waveform?

Simplified Explanation of Fourier Analysis

Fourier analysis works on the principle that a periodic signal can be represented as a sum of a series of sine and cosine waves. It states that the signal can be separated into a spectrum of discrete frequencies deriving from this series .

The Fourier transform takes apart time domain data using projections. It digitizes the signal, x, into a sequence of N numbers. Each sample is a point with a time interval of Δt between them.

The computation calculates the frequency spectra for each sample, including the coefficients that approximate the original signal when combined. Then, it combines the spectra. The resulting set of components is the Fourier transform of x(t).

For a more comprehensive explanation of Fourier analysis, visit the following VRU lessons:

  • Data Analysis
  • Fourier Analysis (FFT)
  • How the PSD is Computed

FFT Analysis in ObserVIEW

FFT analysis in the ObserVIEW software is an efficient method of data analysis. The software responds to any change to the settings with a fast and automatic recalculation of the computed parameters. The software can perform the calculation on live data streaming from Live Analyzer or an imported file.

Features of ObserVIEW’s FFT analysis include:

  • Up to 1,048,576 analysis lines (user-defined)
  • Industry-standard window functions with comprehensive support for the selection process
  • Standard, harmonic, and RMS cursor types and more
  • Quick reporting features, including copy-paste functionality
  • Live computation of data with Live Analyzer
  • AVD conversion (acceleration, velocity, displacement)

FFT Parameters

To add an FFT graph in ObserVIEW, select Add Graph > FFT. The user-defined settings include analysis lines, window function, and data bias range.

ANALYSIS LINES

The sample rate and analysis lines determine the frame length of an FFT. Fewer lines will result in a shorter frame of time data, and more lines will result in a longer frame.

The length of each frame required to generate an FFT sample rate. For pure FFT analysis, the frequency resolution is analysis lines. If the FFT resolution is known, the test engineer can also use 1/FFT resolution to equate the time duration of each FFT frame.

Increasing the number of analysis lines increases the FFT frequency resolution, which is useful when analyzing low-frequency content. Increasing this parameter also results in a higher resolution of the resulting analysis plot. However, higher lines increase the computational burden, and the increased analysis time can result in a slower response to change.

WINDOW FUNCTION

The FFT calculation interprets the two endpoints of a time waveform as though they were connected—i.e., they have the same value at each end of a time interval. However, random signals are rarely equal at each end of the time interval. This assumption creates discontinuities in the time domain and results in unwanted noise in the frequency spectrum.

Window functions are added to the signal-processing algorithm to address these discontinuities. ObserVIEW includes the industry-standard window functions including Blackman, Hamming, and Hanning. The user should select the function that best fits the application or the purpose of the analysis. Here are a few tips when selecting a window function:

  • Select Blackman, Hamming, or Hanning for general vibration analysis
  • Select Rectangular for periodic signals that are shorter than the window length
  • Flat Top provides very accurate amplitude measurements, but the user sacrifices frequency accuracy for better amplitude accuracy
  • Select Exponential for impact testing, burst random shock, and shock analysis

The ObserVIEW Help file also includes a comprehensive table of window functions for assistance with selection.

FFT AVERAGING

The FFT computation relies on averaging to combine the samples’ frequency spectra. Linear averaging weighs the data over the time range equally. This approach is reasonable for analyzing the true data of a time frame but does not necessarily reflect the variation of real-world vibration and can flatten peaks that are potentially damaging. Exponential averaging is a moving average that puts more weight on recent data. As such, exponential averaging is favored when analyzing long or non-stationary signals.