Fourier Integral Transform
Source lecture(s): PHY621 Lec3
Physical Meaning
Replaces a function with its continuous spectrum of frequency components.
Variable Definitions
| Symbol | Meaning |
|---|---|
| \(\hat{f}(k)\) | frequency-space amplitude |
| \(f(x)\) | position-space function |
Assumptions
\(f\) is absolutely integrable; convergence is mean-square.
Derivation
Let discrete frequency spacing \(\Delta k\to dk/2\pi\); sum becomes integral.
Applications
Signal processing, quantum wave packets, diffraction theory.
Connections to Other Equations
- fourier-series
- convolution
- laplace-transform