Transfer Functions

• The ratio of the $z$-transform of the output to the $z$-transform of the input with initial conditions at zero, denoted b]y $H(z)$
• Can also be determined by taking the $z$-transform of the impulse response or difference equation

Zeros and Poles

• Roots of the numerator of $H(z)$ are the zeros
• Roots of the denominator of $H(z)$ are the poles

BIBO Stability

• A system is BIBO stable if its impulse response is absolutely summable
• If all system poles have a magnitude less than one, the system is BIBO stable and has an absolutely summable impulse response

References

• Transfer functions (course handout)