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THD and THD+N Accuracy with Respect to Block Size

Primary Software: LabVIEW Toolkits>>Sound and Vibration Toolset
Primary Software Version: 4.0
Primary Software Fixed Version: N/A
Secondary Software:
Hardware: Modular Instruments>>Dynamic Signal Acquisition and Analysis (DSA)

Problem:
I am performing a Total Harmonic Distortion plus Noise (THD+N) measurement using the Sound and Vibration Toolset in LabVIEW, and it appears that the measurement is more accurate if I take more samples (larger block size).  What block size do I need in order to guarentee a certain degree of accuracy?  Is there an exact formula that relates block size to THD+N accuracy?

Solution:
It is true that the longer the measurement time, the better the accuracy of a THD or THD+N measurement.  This is because these measurements are essentially calculated using the amplitude of the harmonics in the power spectrum (see Frequency Domain Measurement Fundamentals for THD formula).  The relationship can be logically deduced as follows:
  • increase sampling time » increase number of samples
  • increase number of samples » increase frequency resolution
  • increase frequency resolution » increase amplitude resolution
  • increase amplitude resolution » increase THD+N accuracy

Therefore, coming back to the question of whether or not there is an exact formula relating the THD accuracy and block size, the answer is no.  This is because the accuracy is dependent on the signal (i.e. frequency width of harmonic components).  Based on the window used, there will be a minimum block size required to be able to perform the measurement. However, here are some rules of thumb that may also be helpful in helping determine the ideal block size for your test:

  • With the default window (7-term Blackman-Harris), you should use a block size that guarantees that the fundamental frequency is at least greater than 20 times df, where df is the frequency resolution of the FFT.
  • For a standard Hanning window, the measurement can be accomplished with a block size that guarantees that the fundamental frequency is at least 10 times df. This would reduce the measurement time by a factor 2.
  • It is our experience that the default window offers the best measurement accuracy.

The longest measurement time will be at the lowest test frequency. For example, with a test frequency of 20 Hz, this will require a measurement duration of 0.5 s, resulting into a 2 Hz FFT resolution (df), just sufficient for the Hanning window (10 times df or 20 Hz in this case).



Related Links:
NI Developer Zone: Frequency Domain Measurement Fundamentals
Products & Services: Sound and Vibration Measurement and Analysis
Products & Services: NI Sound and Vibration Toolkit
Products & Services: NI Sound and Vibration Measurement Suite 6.0

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Report Date: 02/05/2007
Last Updated: 05/08/2008
Document ID: 464F99JQ

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