Debug Info:
{
  "title": "Fourier Transform",
  "symbol": "ℱ",
  "definition": "The Fourier transform decomposes a function of time into its constituent frequencies.",
  "usage": "Used in signal processing, image analysis, and solving partial differential equations.",
  "examples": [
    {
      "description": "Continuous Fourier Transform",
      "latex": "\\hat{f}(\\xi) = \\int_{-\\infty}^{\\infty} f(x)e^{-2\\pi i x \\xi} dx"
    },
    {
      "description": "Discrete Fourier Transform",
      "latex": "X_k = \\sum_{n=0}^{N-1} x_n e^{-\\frac{2\\pi i}{N}kn}"
    }
  ],
  "tags": [
    "analysis",
    "signal processing",
    "differential equations"
  ],
  "relatedConcepts": [
    "Laplace transform",
    "wavelets",
    "frequency domain"
  ]
}

Fourier Transform

Symbol

ℱ

Definition

The Fourier transform decomposes a function of time into its constituent frequencies.

Usage

Used in signal processing, image analysis, and solving partial differential equations.

Examples

Tags

Related Concepts