Above, we found the rectangular window transform to be the aliased sinc function:

This (real) result is for the

As the sampling rate goes to infinity, the aliased sinc function
approaches the regular *sinc function*

More generally, we may plot both the *magnitude* and *phase*
of the window transform versus frequency:

In audio work, we more typically plot the window transform magnitude on a
*decibel (dB) scale*:

Since the DTFT of the rectangular window approximates the sinc function, it should ``roll off'' at approximately 6 dB per octave, as verified in the log-log plot below:

As the sampling rate approaches infinity, the rectangular-window
transform (
) converges exactly to the sinc function.
Therefore, the departure of the roll-off from that of the sinc
function can be ascribed to *aliasing* in the frequency domain,
due to sampling in the time domain.

Download Intro421.pdf

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Download Intro421_4up.pdf

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