Draw POLE ZERO locations of third order Linear Phase LPF & HPF

To draw the pole-zero locations of a third-order linear phase low-pass filter (LPF) and high-pass filter (HPF), follow these steps:

1. Determine the transfer function of the filters. The transfer function for a third-order LPF can be represented as H(s) = K * (s - z1) * (s - z2) * (s - z3) / (s - p1) * (s - p2) * (s - p3), where s is the complex variable, K is the gain, z1, z2, and z3 are the zeros, and p1, p2, and p3 are the poles. Similarly, the transfer function for a third-order HPF can be represented as H(s) = K * (s - z1) * (s - z2) * (s - z3) / (s - p1) * (s - p2) * (s - p3).

2. Determine the values of the zeros and poles for the LPF and HPF. The zeros and poles can be calculated based on the desired cutoff frequency and filter characteristics.

3. Plot the pole-zero locations on the complex plane. The zeros are represented by 'o' symbols, and the poles are represented by 'x' symbols. The location of each zero or pole is determined by its real and imaginary parts.

4. Connect the zeros and poles with lines to visualize the frequency response of the filter. The lines connecting the zeros and poles indicate the magnitude and phase response of the filter at different frequencies.

5. Label the plot with the corresponding frequencies and filter type (LPF or HPF) for clarity.

By following these steps, you can draw the pole-zero locations of a third-order linear phase LPF and HPF.