Comparing Transforms

Laplace Transform

The Laplace transform is the most comprehensive transform method.

• Uses the complex-frequency domain (the s-domain)
• Works for both transient and steady-state response
• Works in circuits with initial conditions

Fourier Transform

You can convert from the s domain to the frequency domain by simply specifying $s = j\omega$.

• Uses the frequency domain ($\omega$)
• Signals must be periodic and absolutely integrable
• Will not work for initial conditions
• Good for analyzing frequency response

Phasor Analysis

• Uses the phasor domain
• Signals must be sinusoidal
• Only calculates at one frequency