fourier_transform_expression
Transform a space or time-domain expression into its frequency-domain form. Useful for spectral analysis, signal processing, and periodic dosing evaluation.
Instructions
Fourier transform: f(x) → F(k).
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🆕 PHASE 2 - NOT IN SYMPY-MCP OR NSFORGE v0.2.3!
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Transforms spatial/time function to frequency domain.
USE CASES:
- Periodic dosing analysis (repeated administration)
- Spectral analysis (frequency components)
- Signal processing (filter design)
- Diffusion problems (spatial frequency)
Args:
expression: Space/time-domain expression f(x)
space_var: Space/time variable (default: "x")
freq_var: Frequency variable (default: "k")
Returns:
Fourier transform F(k)
Examples:
# Gaussian pulse
fourier_transform_expression("exp(-x**2)", "x", "k")
→ {"result": "sqrt(pi)*exp(-pi**2*k**2)", ...}
# Exponential decay
fourier_transform_expression("exp(-abs(x))", "x", "k")
→ {"result": "2/(1 + k**2)", ...}
# Rectangular pulse
fourier_transform_expression("Heaviside(x+1) - Heaviside(x-1)", "x", "k")
→ {"result": "2*sin(k)/k", ...}
# PK: Periodic dosing spectrum
# Analyze frequency components of repeated doses
Input Schema
TableJSON Schema
| Name | Required | Description | Default |
|---|---|---|---|
| freq_var | No | k | |
| space_var | No | x | |
| expression | Yes |
Output Schema
TableJSON Schema
| Name | Required | Description | Default |
|---|---|---|---|
No arguments | |||