Spectrum Analysis Basic Notation and Principles - The Problem of Leakage

In the example above, a sine function with a frequency of 0.2 was "inserted" into the series. However, because of the length of the series (16), none of the frequencies reported in the spreadsheet exactly "hits" on that frequency. In practice, what often happens in those cases is that the respective frequency will "leak" into adjacent frequencies. For example, you can find large periodogram values for two adjacent frequencies, when, in fact, there is only one strong underlying sine or cosine function at a frequency that falls in-between those implied by the length of the series. There are three ways in which one can approach the problem of leakage:

  1. By padding the series you can apply a finer frequency "roster" to the data,
  2. By tapering the series prior to the analysis you can reduce leakage, or
  3. By smoothing the periodogram you can identify the general frequency "regions" or (spectral densities) that significantly contribute to the cyclical behavior of the series.