What are the zeroes of a transfer function?

The zeroes of a transfer function are defined as the values of s that make the numerator equal to zero. In the context of control systems and signal processing, the transfer function is a mathematical representation of the relationship between the input and output of a linear time-invariant system in the Laplace domain.

When the numerator is zero, it indicates frequencies or values for which the output of the system is zero, regardless of the input. This characteristic is crucial in analyzing system behavior, specifically in determining points of interest in the frequency response, such as frequencies that may lead to cancellation of output signals.

Understanding the zeroes of a transfer function is essential for designing and analyzing systems because they directly influence the system's output and can impact its dynamics, including transient response and stability.