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Three-Term Blackman-Harris Window

The classic Blackman window of the previous section is a three-term window in the Blackman-Harris family ($ L=2$), in which one degree of freedom is used to minimize side-lobe level, and the other is used to maximize roll-off rate. Harris [97, p. 64] defines the three-term Blackman-Harris window as the one which uses both degrees of freedom to minimize side-lobe level. An improved design is given in Nuttall [185, p. 89], and its properties are as follows:

  • $ \alpha_0 = 0.4243801$ $ \alpha_1 = 0.4973406$, and $ \alpha_2 = 0.0782793$.
  • Side-lobe level $ 71.48$ dB.
  • Side lobes roll off $ \approx 6\dB $ per octave in the absence of aliasing (like rectangular and Hamming).
  • All degrees of freedom (scaling aside) are used to minimize side lobes (like Hamming).

Figure 3.8 plots the three-term Blackman-Harris Window and its transform. Figure 3.9 shows the same display for a much longer window of the same type, to illustrate its similarity to the rectangular window (and Hamming window) at high frequencies.

Figure 3.8: Three-term Blackman-Harris window and transform
\includegraphics[width=\twidth]{eps/blackmanHarris3}

Figure 3.9: Longer three-term Blackman-Harris window and transform
\includegraphics[width=\twidth]{eps/blackmanHarris3Long}


Previous: Matlab for the Classic Blackman Window
Next: Frequency-Domain Implementation of the Blackman-Harris Family

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About the Author: Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.


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