Spectrum Analysis Basic Notation and Principles - Tapering

The so-called process of split-cosine-bell tapering is a recommended transformation of the series prior to the spectrum analysis. It usually leads to a reduction of leakage in the periodogram. The rationale for this transformation is explained in detail in Bloomfield (1976, p. 80-94). In essence, a proportion (p) of the data at the beginning and at the end of the series is transformed via multiplication by the weights:

wt = 0.5*{1-cos[π*(t - 0.5)/m]}     (for t=0 to m-1)

wt = 0.5*{1-cos[π*(N - t + 0.5)/m]}     (for t=N-m to N-1)

where m is chosen so that 2*m/N is equal to the proportion of data to be tapered (p).