FSV detail (from IEEE EMC Symposium 2005)

 

The structure of the FSV involves reading the two data files to be compared and interpolating them over the common window (often common frequency range) so that the data-points to be compared are coincident.  This approach ensures that like is being compared with like and will not affect the overall results unless the data are severely under sampled.  It must be remembered that the purpose of the FSV is to mimic a visual comparison and so long as any interpolation does not produce visually different results, the approach is perfectly acceptable.

 

The actual comparison is based on decomposing the original data into trend information and feature information.  So the next step is to Fourier Transform the data and window the transformed data to separate out the lower and higher portions of the data.  The high and low portions are then inverse transformed back into the original domain.  Combinations of these filtered data sets and their derivatives are used to compute the Amplitude Difference Measure (ADM) and the Feature Difference Measure (FDM): which can be combined into the Global Difference Measure (GDM). 

 

More specifically, the procedure is:

 

  1. Read data, obtain the overlap window and interpolate the data, if necessary, in the overlap region to ensure coincident pairs of data points.  This ensures that that the two data sets to be compared have the same number of data points located at the same positions on the independent (x) axis. 

 

  1. Fourier Transform both data sets.  Depending on whether a Fast or Discrete approach is used, this may require sufficient zero padding to enable conversion.

 

  1. Calculate the ‘low’ data sets using the transformed data.
    1. Ignore the first four data points in the transformed set (in order to avoid DC and very low frequency components) and sum the intensities of the remaining data.
    2. Obtain a 40% location by summing the data from the fifth point (i.e. ignoring the near-DC data) until the total reaches 40% of the total value calculated in step 3a.  The ‘40%’ location used by the FSV is the lowest of the two resulting numbers (from the two original data sets). A ‘break-point’ five data points above this is returned – a value that allows a comfortable transition window between the low and the high results.
    3. Window the transformed data for both data sets by taking a linearly decreasing envelope from three (or five) points below the break-point to three (or five) points above it.  Essentially, low-pass filtering the transformed data
    4. Inverse transform the windowed data to give the ‘low region’ data for both original data sets. (Lo1(f) and Lo2(f)  it is assumed for ease of representation that the original data is frequency domain based, although it could equally well be time domain or space domain based)

 

  1. Calculate the ‘high’ data sets using the transformed data.  Repeat the process from 3c, by applying the opposite envelope to the transformed data: essentially high pass filtering it.  This data is then inverse transformed to give the ‘high region’ data for both of the original data sets. (Hi1(f) and Hi2(f) again assuming frequency domain for ease of representation)

 

  1. Calculate the ADM on a point-by-point basis. Given that each data set has N points and, at an arbitrary data point f, the ADM is calculated from the following equation.  This point-by-point representation can be abbreviated ADMi

 

     (1)

 

  1. Calculate the single value of ADM.  A mean value of the ADM(f) gives an overall, single figure, goodness-of-fit.  It is obtained from the following equation, noting that fmin­ and fmax are the lower and upper limits for the data range.  Note: a median value, rather than a mean value has demonstrated some improvements in agreement with visual interpretations.

 

                              (2)

 

  1. Calculate the ADM confidence histogram.  The range of values for the ADM, and, in fact, the FDM and GDM  can be divided into six categories, each with a natural language descriptor: Excellent, Very Good, Good, Fair, Poor, Very Poor.  These are the terms that are most often used in descriptions of the quality of comparisons.  The confidence histogram, like a probability density function, provides some intelligence as to how much emphasis can be placed on the single figure of merit.  There is some evidence to show that this mirrors the overall group assessment of any data pair by a number of engineers.  The determination of the histogram is simply a case of counting the proportion of points that fall into one of the categories, according to the rule base in the following table.
  2.  

FSV interpretation scale

FSV value (quantitative)

FSV interpretation (qualitative)

Less than 0.1

Excellent

Between 0.1 and  0.2

Very good

Between 0.2 and 0.4

Good

Between 0.4 and 0.8

Fair

Between 0.8 and 1.6

Poor

Greater than 1.6

Very poor

 

  1. Calculate derivatives in preparation for the FDM calculation.  The following components need to be calculated:  The first derivatives of the Lo(f) and Hi(f) data sets and the second derivatives of the Hi(f) data sets.  The derivatives accentuate the high rate-of-change features in the original data and differences based on the derivatives are combined in the determination of the FDM.  The first derivatives are currently obtained by a simple difference approach (i.e. ignoring the x-axis data) so, for example, Lo’(f) = Lo(f+2) – Lo(f-2).  The second derivatives of the Hi data sets are obtained from the first derivatives using a simple difference scheme again, in this case, Hi”(f)  = Hi’(f+3) – Hi’(f-3).  This simple difference approach was used in the original formulation and in the current free-standing application produced by the authors.

 

  1. Calculate the point-by-point FDM. The FDM is formed from three parts based on the derivatives calculated in step 8.

 

       (3)

 

        (4)

 

      (5)

 

   (6)

 

  1. Calculate the single value of FDM.  This is done in exactly the same way as for the ADM.

 

  1. Calculate the FDM confidence histogram.  This is dome in exactly the same way as was done for the ADM.

 

  1. Obtain the point-by-point GDM value.  The GDM is premised on the ADM and FDM being largely independent, which means that:

 

      (7)

 

  1. Calculate the overall GDM value and the GDM confidence histogram.  This follows the same procedure as the ADM and FDM.

 

  1. Determine the equivalent visual scale values for ADM, FDM, and GDM.  The FSV values can be scaled to a visual six point scale (where Excellent = 1 and Very poor = 6).  The piece-wise approach for this is given in Table II, where X is the ADM, FDM or GDM (total or point-by-point):

 

Piecewise visual conversion

If X £ 0.1 Then V = 1 +10X

If X > 0.1 and X £ 0.2 Then V = 2 + 10(X – 0.099)

If X > 0.2 and X £ 0.4 Then V = 3 + 5(X – 0.199)

If X > 0.4 and X £ 0.8 Then V = 4 + 2.5(X – 0.399)

If X > 0.8 and X £ 1.6 Then V = 5 + 1.25(X – 0.799)

If X > 1.6 Then V = 6

 

 

 

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