High Pass Filter (HPF)

A high pass filter is a complement of a low pass filter in that the frequency range from o to ωc is the SB and from ωc to infinity is the PB.

fig: high pass filter

\[
|H(\omega)| = 
\begin{cases} 
0 & \text{for } -B \leq \omega \leq B \\[6pt]
1 & \text{for } |\omega| > B
\end{cases}
\]

fig: Gain and Attenuation Relation

where, ω c ​ is the cutoff frequency