Difference equation when transfer function expressed as poles and zeros

1. What is the difference between zeros and poles of a transfer function?
2. What is the difference between poles and zero?
3. How do you find the transfer function from the difference equation?
4. How do you plot poles and zeros of a transfer function?

What is the difference between zeros and poles of a transfer function?

Poles and Zeros of a transfer function are the frequencies for which the value of the denominator and numerator of transfer function becomes zero respectively. The values of the poles and the zeros of a system determine whether the system is stable, and how well the system performs.

What is the difference between poles and zero?

Definition: Poles are the roots of the denominator of a transfer function. Zeros are the roots of the nominator of a transfer function.

How do you find the transfer function from the difference equation?

To find the transfer function, first take the Laplace Transform of the differential equation (with zero initial conditions). Recall that differentiation in the time domain is equivalent to multiplication by "s" in the Laplace domain. The transfer function is then the ratio of output to input and is often called H(s).

How do you plot poles and zeros of a transfer function?

In the general case of a transfer function with an mth order numerator and an nth order denominator, the transfer function can be represented as: The pole-zero representation consists of the poles (p_i), the zeros (z_i) and the gain term (k). Note: now the step of pulling out the constant term becomes obvious.