Generalized Hamming Window Family

The *generalized Hamming window family* is constructed by
multiplying a rectangular window by one period of a cosine. The
benefit of the cosine tapering is *lower side-lobes*. The price
for this benefit is that the *main-lobe doubles in width*. Two
well known members of the generalized Hamming family are the
*Hann* and *Hamming* windows, defined below.

The basic idea of the generalized Hamming family can be seen in the frequency-domain picture of Fig.3.8. The center dotted waveform is the aliased sinc function (scaled rectangular window transform). The other two dotted waveforms are scaled shifts of the same function, . The sum of all three dotted waveforms gives the solid line. We see that

- there is some cancellation of the side lobes, and
- the width of the main lobe is doubled.

In terms of the rectangular window transform (the zero-phase, unit-amplitude case), this can be written as

(4.15) |

where , in the example of Fig.3.8.

Using the shift theorem (§2.3.4), we can take the inverse transform of the above equation to obtain

(4.16) |

or,

Choosing various parameters for and result in different windows in the generalized Hamming family, some of which have names.

- Hann or Hanning or Raised Cosine
- Matlab for the Hann Window
- Hamming Window
- Matlab for the Hamming Window
- Summary of Generalized Hamming Windows
- The MLT Sine Window

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