Low Pass Filter (LPF)

A low-pass filter is a device or system that attenuates (reduces) the amplitude of signals with frequencies higher than the cutoff frequency while allowing signals with frequencies lower than or equal to the cutoff frequency to pass through.

Characteristics: where Pass band Extends from w=0 to w=w_c where w_c = cut off frequency.

fig: Low pass filter

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

fig: Gain and Attenuation Relation

where ω c ​ is the cutoff frequency.