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Numeric Summary (FFT)

This option offers a full FFT report.

Initial Information

The following information is always included:

  • Main, x, and y data titles
  • File source for data
  • Report date
  • FFT algorithm selected
  • Data tapering window used (if present)
  • Size of data
  • Size of FFT and prime factorization
  • Total power of spectrum, SSA, MSA, TISA
  • Signal count detected
  • Linear trend removal state

Interpolated Spectral Peaks

The first optional item, available from the Format menu, is Add Interpolated Spectral Peaks. The bin-interpolated peaks, based upon the signal count, are listed. This table will consist of interpolated spectral frequencies and interpolated values for whichever spectral quantity is being plotted. Note that the dB Norm format normalizes to 0 dB with the actual spectral data series. The peak corresponding to this 0 dB channel will typically report a positive dB value because of the bin interpolation.

Frequency Analysis

The second optional item is Add Frequency Analysis. This table also uses interpolated frequencies and computes interpolated amplitudes and phases (sine-based). For each peak, the TISA power (based on amplitude) is computed. Note that spectral leakage to other bins will reduce the power reported for each component.

Absolute and relative percents are also given. These are often the quantities of interest when comparing strengths of signal components. The summed power reported in the frequency analysis is merely the sum of the component powers. It is not the power of the composite signal that would result from the addition of the components. In most instances, this sum will be lower than the TISA power of the incoming data.

Linear Sine Component Fit

When the Add Sine Component Linear Fit Summary item in the Format menu is checked, a linear sinusoidal least-squares fit is made to the incoming data. The report will then include a summary of this suboptimal sinusoidal parametric regression. In this linear fit, the sinusoid count is set to the number of spectral peaks identified in the procedure and the frequencies are locked at the values determined from the spectrum. For this procedure, the frequencies will derive from the interpolated values found from the FFT. In general, an FFT is not a particularly accurate frequency estimator even with a good bin interpolation algorithm. Further, the limited spectral resolution of the FFT may result in more than one component appearing as a single spectral peak.

Since the amplitudes and phases are determined from the sinusoidal parametric model, the influence of spectral leakage is no longer a factor.

If the Add Sine Component Linear Fit Details item is checked, the report will also include a statistical breakdown of each sinusoid in the fit.