GLOSSARY OF TERMS USED IN TIME SERIES ANALYSIS
OF CARDIOVASCULAR DATA
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DATA-WINDOW

A function of time that is multiplied by a data segment. It is mainly used before computing the FFT spectrum of the data segment, and its purpose is to smooth or otherwise shape the resulting spectrum.

In fact, the Fourier transform is theoretically defined for signals of infinite duration, and thus a finite segment of data is treated as a periodic signal with period equal to the duration of the data segment. Differences between the starting and ending values of the segment produces a discontinuity which generates high-frequency spurious components. These can be reduced tapering down start and end of the segment by multiplying the signal by a data window w(t). Popular data windows in the analysis of blood pressure and heart rate variabilities are the 10% cosine-taper and  the Hann windows. Data windowing, however, worsens frequency resolution and estimation variance of the spectrum.

Definitions of Typical N-point Discrete Time Windows
Type
Definition
Rectangular w(k)=1                                        0 k N-1
Triangular (or Bartlett)
10% Cosine-taper
Hann1
Hamming2

Series of 100 R-R intervals in a healthy subject before (left) and after data windowing by the 10% cosine-taper (centre) or by the Hann window (right). Lower panels: shapes of the corresponding data windows.
Notes (from http://www.cg.tuwien.ac.at/research/vis/vismed/Windows )
1 The Hann window is due to Julius van Hann, but it is often wrongly referred to as Hanning window
2  The Hamming window is due to Richard Wesley Hamming

Reference
Marple SL Jr.(1987) Digital spectral analysis with applications. Prentice Hall, Englewood Cliffs, New Jersey

(PC 07-09-1999)

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