陆昱宽

Sources:

1. B. P. Lathi & Roger Green. (2018). Chapter 4: The Laplace Transform. Signal Processing and Linear Systems (3rd ed., pp. 360-370). Oxford University Press.

The time-differentiation property of the Laplace transform has set the stage for solving linear differential (or integro-differential) equations with constant coefficients.

Because \(d^k y / d t^k \Longleftrightarrow\) \(s^k Y(s)\), the Laplace transform of a differential equation is an algebraic equation that can be readily solved for \(Y(s)\).

Next we take the inverse Laplace transform of \(Y(s)\) to find the desired solution \(y(t)\).

Sources:

1. B. P. Lathi & Roger Green. (2018). Chapter 4: The Laplace Transform. Signal Processing and Linear Systems (3rd ed., pp. 350-360). Oxford University Press.

For a quick reference table, see Wikipedia page on the Laplace transform.

Sources:

1. B. P. Lathi & Roger Green. (2018). Chapter 4: The Laplace Transform. Signal Processing and Linear Systems (3rd ed., pp. 338-345). Oxford University Press.

Sources:

1. B. P. Lathi & Roger Green. (2018). Chapter 4: The Laplace Transform. Signal Processing and Linear Systems (3rd ed., pp. 330-404). Oxford University Press.

Source:

1. Exploring Parallel Strategies with Jax
2. Training Deep Networks with Data Parallelism in Jax

Source: Trigonometric Identities

Sources:

1. B. P. Lathi & Roger Green. (2021). Chapter 2: Time-Domain Analysis of Continuous-Time Systems. Signal Processing and Linear Systems (2nd ed., pp. 163-167). Oxford University Press.

Sources:

1. B. P. Lathi & Roger Green. (2021). Chapter 3: Signal Representation by Fourier Series. Signal Processing and Linear Systems (2nd ed., pp. 261-277). Oxford University Press.

Sources:

B. P. Lathi & Roger Green. (2018). Chapter 7: Continuous-Time Signal Analysis. Signal Processing and Linear Systems (3nd ed., pp. 689-701). Oxford University Press.

For convenience, we now introduce a compact notation for the useful gate, triangle, and interpolation functions.

For more results, refer to Table of the Fourier Transform Pairs.

Sources:

1. B. P. Lathi & Roger Green. (2021). Chapter 3: Signal Representation by Fourier Series. Signal Processing and Linear Systems (2nd ed., pp. 286-301). Oxford University Press.