Summary of Generalized Hamming Windows

**Definition:**

(4.20) |

where

(4.21) |

**Transform:**

(4.22) |

where

(4.23) |

**Common Properties**

- Rectangular + scaled-cosine window
- Cosine has one period across the window
- Symmetric ( zero or linear phase)
- Positive (by convention on and )
- Main lobe is radians per sample wide, where
- Zero-crossings (``notches'') in window transform at intervals of outside of main lobe

Figure 3.12 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.

**Rectangular window properties:**

- Abrupt transition from 1 to 0 at the window endpoints
- Roll-off is asymptotically dB per octave (as )
- First side lobe is dB relative to main-lobe peak

**Hann window properties:**

- Smooth transition to zero at window endpoints
- Roll-off is asymptotically -18 dB per octave
- First side lobe is dB relative to main-lobe peak

**Hamming window properties:**

- Discontinuous ``slam to zero'' at endpoints
- Roll-off is asymptotically -6 dB per octave
- Side lobes are closer to ``equal ripple''
- First side lobe is
dB down =
dB better than
Hann
^{4.7}

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