Frequency Response Visualization

The magnitude response of a linear system is the intersection of the magnitude of the transfer function, $\left|H\left(s\right)\right|$, in the $s=\sigma +j\omega$-plane and the plane containing the $j\omega$-axis, as shown in Figs. 1-4. Note that the poles are the values of $s$ that makes $\left|H\left(s\right)\right|\rightarrow \infty$, and the zeros are values of $s$ that result in $\left|H\left(s\right)\right|=0$.

Figure 1: The low-pass Butterworth filter frequency response.	Figure 2: The low-pass Chebyshev Type-I filter frequency response.
Figure 3: The low-pass Chebyshev Type-II filter frequency response.	Figure 3: The low-pass Elliptic filter frequency response.
Figure 3: The low-pass Bessel filter frequency response.