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