The DOF value increases linearly with each new FFT frame until the desired value is reached. The number will depend on the type of window function.
#DEGREE OF FREEDOM IN STATISTICS UPDATE#
And, at a 4x update rate, each frame’s DOF contribution is smaller than the amount at the 2x update rate. At a 2x update rate (50% overlap), each frame is < 2 DOF. At a 1x update rate (0% overlap), each frame equals exactly 2 DOF. The update rate (also called overlap percentage) changes the required step size between each FFT frame block with respect to the window type. For example, a 100 DOF test will take about 50 sec at level to reach the desired amount of averaging.Īn update interval of 1.0 sec for a random test. An update interval of 1.0 sec means the DOF will update at roughly 2 DOF/sec. The following image displays a typical set of random test settings. Therefore, the effective DOF for a given time interval can be doubled by applying a 50% overlap. A 75% overlap achieves a DOF of about 1x the number of frames. Generally, with a 50% overlap and a window function, the DOF is close to 2x the number of frames. The following DOF calculator can be used to assess the probability of a random vibration test being within tolerance. Instead, the DOF can be estimated by simulating data with the specified overlap and window function applied, computing the statistics of the resulting PDF, and comparing the statistics to a Chi-squared distribution with a known DOF. As such, the effective DOF of the average is no longer a multiple of the number of frames. However, when frames are overlapped and window functions are applied, the frames are no longer independent. When frames of data are assumed to be independent, the DOF equals 2x the number of frames. Time to acquire (N) DOF with 50% overlap = 0.25 * (N) * (lines) / (maxfreq) **Note: for DOF calculations to be accurate, the time waveform must be stationary.** Window Functions and Overlap Reaching the defined value may require the adjustment of several test settings such as window functions and overlap. Often, vibration test specifications will define the desired DOF. A more detailed explanation of the calculation of the averaged random can be found here. Thus, confidence intervals and the probability of meeting tolerance can be computed from the equations that define the chi-squared distribution. In short, the averaged PSD of a Gaussian waveform is a chi-squared distributed random variable with (2*F) DOF, where F is the frames of time data. This property derives from the computation of an averaged random power spectral density (PSD) using the fast Fourier transform (FFT).
Statistical degrees-of-freedom (DOF) is relevant when performing random vibration testing. What is statistical degrees-of-freedom? How do you achieve a defined DOF value? ANSWER An understanding of the DOF calculation will help to clarify the purpose of the defined value. Statistical DOF help to define confidence intervals and the probability of meeting tolerance. Random vibration test specifications are likely to specify a degrees-of-freedom (DOF) value.
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