Gain at given frequency from $z$-plane zero-pole plot. Two methods gives different results

1. How do poles and zeros affect frequency response?
2. Is it possible to plot the pole-zero using Z transform?
3. What does pole zero plot tell us?
4. How do poles and zeros affect transfer function?

How do poles and zeros affect frequency response?

A pole frequency corresponds to a corner frequency at which the slope of the magnitude curve decreases by 20 dB/decade, and a zero corresponds to a corner frequency at which the slope increases by 20 dB/decade.

Is it possible to plot the pole-zero using Z transform?

Once the poles and zeros have been found for a given Z-Transform, they can be plotted onto the Z-Plane.

What does pole zero plot tell us?

A pole-zero plot shows the location in the complex plane of the poles and zeros of the transfer function of a dynamic system, such as a controller, compensator, sensor, equalizer, filter, or communications channel.

How do poles and zeros affect transfer function?

Addition of poles to the transfer function has the effect of pulling the root locus to the right, making the system less stable. Addition of zeros to the transfer function has the effect of pulling the root locus to the left, making the system more stable.