A ComfyUI custom node that computes the Fractional Fourier Transform (FrFT) of an image and outputs its magnitude spectrum.
The Fractional Fourier Transform is a generalization of the standard Fourier transform parameterized by an order a. It continuously rotates a signal in the time–frequency plane:
| Order | Result |
|---|---|
0.0 |
Identity (input magnitude) |
0.5 |
Midpoint between spatial and frequency domains |
1.0 |
Standard DFT spectrum (equivalent to FFT) |
2.0 |
Spatially reversed image |
Intermediate values produce spectra that blend spatial and frequency information, useful for analyzing signals with time-varying frequency content.
- Clone or copy this repository into your ComfyUI custom nodes directory:
ComfyUI/custom_nodes/ComfyUI_FrFT/ - Restart ComfyUI. The node will appear automatically.
Dependencies: numpy (already bundled with ComfyUI).
Category: image/transform
| Name | Type | Default | Description |
|---|---|---|---|
image |
IMAGE | — | Input image tensor [B, H, W, C] |
order_x |
FLOAT (0–4) | 1.0 |
FrFT order along the x-axis (columns) |
order_y |
FLOAT (0–4) | 1.0 |
FrFT order along the y-axis (rows) |
log_scale |
BOOLEAN | True |
Apply log(1 + |F|) compression before normalization |
channel_mode |
ENUM | luminance |
luminance: convert to grayscale first; per_channel: process each RGB channel independently |
| Name | Type | Description |
|---|---|---|
spectrum |
IMAGE | Magnitude spectrum normalized to [0, 1], shape [B, H, W, 3] |
The implementation follows the Ozaktas–Arikan–Kutay–Bozdagi (1996) fast discrete FrFT algorithm:
- Reduce the order
ato the core interval(0.5, 1.5)using FFT/IFFT steps. - Apply chirp premultiplication:
g[n] = f[n] · exp(−iπ tan(φ/2) · n² / N) - Convolve with a chirp kernel via zero-padded FFT:
h[k] = exp(iπ k² / (N sin φ)) - Apply chirp postmultiplication (same chirp as step 2).
- Scale by
exp(−iπ(1−a)/4) / sqrt(N |sin φ|).
The 2D transform is separable: 1D FrFT is applied along rows first, then columns.
Reference: H. M. Ozaktas, O. Arikan, M. A. Kutay, G. Bozdagi, "Digital Computation of the Fractional Fourier Transform," IEEE Transactions on Signal Processing, vol. 44, no. 9, pp. 2141–2150, 1996.
- The algorithm is approximately unitary: norm preservation error is < 1% for smooth signals near
a = 1, and up to ~15% at boundary orders (a = 0.5,a = 1.5) due to finite-length discretization effects. This is expected behavior of the Ozaktas discrete FrFT and does not affect visual quality. - Additivity (
F_a ∘ F_b ≈ F_{a+b}) holds to within ~0.7% relative error for smooth signals. - For purely visual spectrum analysis, all order values produce meaningful and correct results.
MIT