Truncated-Sinc Interpolation

Truncate sinc$(t)$ at 5th zero-crossing to left and right of time 0 to get the following amplitude response:

Truncated-Sinc Transform

• Vertical axis in dB, horizontal axis in spectral samples
• Optimal in least-squares sense
• Poor stop-band rejection ( $\approx 20$ dB)
• ``Gibbs Phenomenon'' gives too much ``ripple''
• Ripple can be reduced by tapering the sinc function to zero instead of simply truncating it