## Rectangular Window

The rectangular window was discussed in Chapter 4 (§4.5). Here we summarize the results of that discussion.

**Definition ( odd):**

**Transform:**

The DTFT of a rectangular window is shown in Fig.3.1.

**Properties:**

- Zero crossings at integer multiples of
- Main lobe width is .
- As increases, the main lobe narrows (better frequency resolution).
- has
*no effect on the height of the side lobes*(same as the ``Gibbs phenomenon'' for truncated Fourier series expansions). - First side lobe only 13 dB down from the main-lobe peak.
- Side lobes roll off at approximately 6dB per octave.
- A
*phase term*arises when we shift the window to make it*causal*, while the window transform is real in the zero-phase case (*i.e.*, centered about time 0).

**Next Section:**

Generalized Hamming Window Family

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Spectral Interpolation