Window Functions and Spectral Leakage - Signal Processing of Random Physiological Signals - page 186

1 dB

1.2

-20

1.0

-40

0 T -n bins 0 n bins

(a) (b)

FIGURE 16.7 : Parzen/Rietz window. Trace (a) is the time domain weighted coefficients. Trace
(b) shows the main frequency lobe and the resulting side lobes. The first sidelobe is − 21 dBs from

the peak of the frequency main lobe

Characteristics of the rectangular window performance are − 13 dB of the first side

lobe from the height of the main lobe with a 6 dB/octave fall-off rate, 1.00 coherence

gain, and 3.92-dB scallop loss (3.92-dB worst case process loss).

−

16.3.3 Parzen/Rietz Window
The Parzen/Rietz window is the simplest continuous polynomial window. The mathe-
matical model is shown in (16.2).

( i − 0 . 5( N − 1))

x ( i ) = 1 − (16.2)

0 . 5( N − 1)

The Parzen/Rietz window gives a smoother representation than the Hamming
window; however, the first side lobe decrease is only 21 dB. The window exhibits a dis-

continuous first derivative at the boundaries, so the roll-off per octave is

−

12 dB/octave.
The Parzen window time domain weighted coefficients are shown in Fig. 16.7(a), with
its resulting Log-magnitude of the Fourier transform shown in Fig. 16.7(b).

−

16.3.4 The Tukey Family of Windows
The Tukey window can be described as a cosine lobe of width, (alpha/2)( N ), convolved
with a rectangle window of width, (1.0 to alpha/2)/ N . The term alpha represents a