Lu, Yukuan

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.

Sources:

1. B. P. Lathi & Roger Green. (2021). Chapter 3: Signal Representation by Fourier Series. Signal Processing and Linear Systems (2nd ed., pp. 297-300). Oxford University Press.

Sources:

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. 193-195). Oxford University Press.

In this section I will illustrate that, for a system specified by the differential equation \[ \begin{equation} \label{eq_2_2} Q(D) y(t)=P(D) x(t) , \end{equation} \]

its transfer function is \(H(s)\), the bilateral Laplace transform of \(h(t)\), which is the unit impulse response of the system, and that \(H(s)\) also satisfies: \[ \color{teal} {H(s)=\frac{P(s)}{Q(s)}} . \]

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. 168-195). Oxford University Press.

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. 151-162). Oxford University Press.