Common Properties

• Window is a rectangular window plus a scaled cosine, where the cosine has one period across the window.
• Symmetric ( $\Rightarrow$ zero or linear phase)
• Positive (by convention on $\alpha$ and $\beta$)
• Main lobe is $4\Omega_M$ radians per sample wide, where $\Omega_M\isdef 2\pi/M$.
• Zero-crossings (``notches'') in window transform at intervals of $\Omega_M$ outside of main lobe.

Figure 3.6 compares the window transforms for the rectangular, Hann, and Hamming windows. Note how the Hann window has the fastest roll-off while the Hamming window is closest to being equal-ripple. The rectangular window has the narrowest main lobe.

Figure 3.6: Comparison of window transforms for the rectangular, Hann, and Hamming windows.