Next Page Previous Page Home Tools & Aids Search Handbook
1. Exploratory Data Analysis
1.3. EDA Techniques
1.3.3. Graphical Techniques: Alphabetic Spectral Plot

Spectral Plot: Sinusoidal Model

Spectral Plot for Sinusoidal Model spectral plot for sinusoidal model
Conclusions We can make the following conclusions from the above plot of the LEW.DAT data set.
  1. There is a single dominant peak at approximately 0.3.
  2. There is an underlying single-cycle sinusoidal model.
Discussion This spectral plot shows a single dominant frequency. This indicates that a single-cycle sinusoidal model might be appropriate.

If one were to naively assume that the data represented by the graph could be fit by the model

    \[ Y_{i} = A_0 + E_{i} \]
and then estimate the constant by the sample mean, the analysis would be incorrect because
  • the sample mean is biased;
  • the confidence interval for the mean, which is valid only for random data, is meaningless and too small.
On the other hand, the choice of the proper model
    \[ Y_{i} = C + \alpha\sin{(2\pi\omega t_{i} + \phi)} + E_{i} \]
where α is the amplitude, ω is the frequency (between 0 and .5 cycles per observation), and \( \phi \) is the phase, can be fit by non-linear least squares. The beam deflection data case study demonstrates fitting this type of model.
Recommended Next Steps The recommended next steps are to:
  1. Estimate the frequency from the spectral plot. This will be helpful as a starting value for the subsequent non-linear fitting. A complex demodulation phase plot can be used to fine tune the estimate of the frequency before performing the non-linear fit.

  2. Do a complex demodulation amplitude plot to obtain an initial estimate of the amplitude and to determine if a constant amplitude is justified.

  3. Carry out a non-linear fit of the model

      \[ Y_{i} = C + \alpha\sin{(2\pi\omega t_{i} + \phi)} + E_{i} \]
Home Tools & Aids Search Handbook Previous Page Next Page