Details

An ideal -band discrete filter is a non-realizable filter whose magnitude response takes a single nonzero value in its passband. For example, an ideal lowpass filter passes frequencies below some cut-off frequency and blocks the others; its passband is thus the interval .

The impulse response of an ideal lowpass -band filter is a sinc sequence; its unit-norm version is

for .

The impulse response at is thus (see figure).

The magnitude response of a unit-norm is (see figure)

for , and 0 otherwise.

References

[1] M. Vetterli, J. Kovačević, and V. K. Goyal, Foundations of Signal Processing, Cambridge: Cambridge University Press, 2014. www.fourierandwavelets.org.

[2] Wikipedia. "Sinc Filter." (Nov 10, 2014) en.wikipedia.org/wiki/Sinc_filter.