### 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

**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}

**Next Section:**

The MLT Sine Window

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Matlab for the Hamming Window