Cho đáp ứng tần số của bộ lọc thông cao lý tưởng lý tưởng pha không ( − π ≤ ω ≤ π ) Đáp ứng xung h ( n ) được xác định như sau:

$h\left(n\right)=-1+\delta \left(n\right)=\left[\frac{\omega {}_{c2}}{\pi }\frac{\text{s}\text{i}\text{n}\omega {}_{c2}n}{\omega {}_{c2}n}=\frac{\omega {}_{c1}}{\pi }\frac{\text{s}\text{i}\text{n}\omega {}_{c1}n}{\omega {}_{c1}n}\right]$

$h\left(n\right)=\delta \left(n\right)+\left[\frac{\omega {}_{c2}}{\pi }\frac{\text{s}\text{i}\text{n}\omega {}_{c2}n}{\omega {}_{c2}n}-\frac{\omega {}_{c1}}{\pi }\frac{\text{s}\text{i}\text{n}\omega {}_{c1}n}{\omega {}_{c1}n}\right]$

$h\left(n\right)=\delta \left(n\right)-\left[\frac{\omega {}_{c2}}{\pi }\frac{\text{s}\text{i}\text{n}\omega {}_{c2}n}{\omega {}_{c2}n}+\frac{\omega {}_{c1}}{\pi }\frac{\text{s}\text{i}\text{n}\omega {}_{c1}n}{\omega {}_{c1}n}\right]$

$h\left(n\right)=\delta \left(n\right)-\left[\frac{\omega {}_{c2}}{\pi }\frac{\text{s}\text{i}\text{n}\omega {}_{c2}n}{\omega {}_{c2}n}-\frac{\omega {}_{c1}}{\pi }\frac{\text{s}\text{i}\text{n}\omega {}_{c1}n}{\omega {}_{c1}n}\right]$