### Three-Term Blackman-Harris Window

The classic Blackman window of the previous section is a three-term
window in the Blackman-Harris family (), 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:

- , and .
- Side-lobe level dB.
- Side lobes roll off 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.

**Next Section:**

Frequency-Domain Implementation of the Blackman-Harris Family

**Previous Section:**

Matlab for the Classic Blackman Window