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Notes › ENGR 2341: Signals and Systems Lecture 19

Transfer Functions

calendar_today April 1, 2025 article 88 words access_time 1 min replay Modified April 1, 2025

Table of Contents

Transfer (System) Functions

The ratio of the Laplace transform of the system output to the Laplace transform of the system input

$$H(s) = \frac{Y(s)}{X(s)}$$

Can also be determined by taking the Laplace transform of the impulse response or from differential equations describing the system

$$H(s) = \int_{-\infty}^{\infty}h(t)e^{-st} \ \mathrm{d}t$$

Poles and Zeros

Roots of $Y(s)$ are the system zeros
Roots of $X(s)$ are the system poles ($\mathcal{P}$)

$$\forall p \in \mathcal{P}, \Re(p) < 0 \implies \int_{-\infty}^{\infty} |h(t)| \, dt < \infty \implies \text{BIBO stability}$$

References

Transfer functions (course handout)

Sources

Transfer functions

Graph

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