Window Functions and Spectral Leakage - Signal Processing of Random Physiological Signals - page 176

FIGURE 16.1 : Sinusoidal waveform. The sine function fits perfectly in the window, since its
value is zero (0) at the beginning and end of the observation interval
Outward leakage can be easily demonstrated by some simple examples. Figure 16.3
shows the Power Spectral Density (PSD) of a sinusoidal with a period that is equal to
the observation window length of 1 second. Note that there is only one lobe at 1 Hz.
Figure 16.4 shows the Power Spectral Density (PSD) of a sinusoidal with a period
that is not equal to the observation window length of 1 second. Note the main-lobe
spectral energy at 0.59 Hz with side lobes at 0.41, 0.50, 0.68, and 0.77 Hz.
In dealing with random physiological data, the possibility of an integral funda-
mental frequency repetition is very limited; hence, regardless of what sampling window
interval is used, leakage will be present in the spectra.
16.1 GENERALITIES ABOUT WINDOWS
The window functions (often called restoring functions) are basically weighting functions
applied to the time domain data. Weighting function selection can be made early in
the design process because the choices of FFT algorithm and weighting function are
independent of each other. Choice of a weighting function to provide the specified
FIGURE 16.2 : Discontinuity in sinusoidal waveform