Window Functions and Spectral Leakage - Signal Processing of Random Physiological Signals - page 177

FIGURE 16.3 : Power spectral density of the trace in Fig. 16.1. Note the main lobe at 1 Hz
without any side lobes
side-lobe level is done without concern for the FFT algorithm that will be used because
1. they work for any length FFT,
2. they work the same for any FFT algorithm, and
3. they do not alter the FFT ability to distinguish two frequencies (resolution).
Window functions, w ( t ), have the following properties:
1. The w ( t ) function has to be real, even and nonnegative.
2. The transformed function has to have a main lobe at the origin of the fundamental
frequency, and side lobes at both sides to ensure symmetry.
3. If the n th derivative has an “impulse” character, then the peak of the side lobes
of the transformed function will decay asymptotically as 6* n dB/octave (least
estimate).
FIGURE 16.4 : Power spectral density of the trace with discontinuity shown in Fig. 16.2. Note
the main lobe of the spectra at 0.59 Hz with side lobes at 0.41, 0.50, 0.68, and 0.77 Hz