ComfyUI_FrFT

A ComfyUI custom node that computes the Fractional Fourier Transform (FrFT) of an image and outputs its magnitude spectrum.

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What is the FrFT?

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.

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Installation

1. Clone or copy this repository into your ComfyUI custom nodes directory:

   ComfyUI/custom_nodes/ComfyUI_FrFT/
   

2. Restart ComfyUI. The node will appear automatically.

Dependencies: numpy (already bundled with ComfyUI).

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Node: FrFT Spectrum

Category: image/transform

Inputs

| 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 |

Output

| Name | Type | Description | |------|------|-------------| | spectrum | IMAGE | Magnitude spectrum normalized to [0, 1], shape [B, H, W, 3] |

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Algorithm

The implementation follows the Ozaktas–Arikan–Kutay–Bozdagi (1996) fast discrete FrFT algorithm:

1. Reduce the order a to the core interval (0.5, 1.5) using FFT/IFFT steps.
2. Apply chirp premultiplication: g[n] = f[n] · exp(−iπ tan(φ/2) · n² / N)
3. Convolve with a chirp kernel via zero-padded FFT: h[k] = exp(iπ k² / (N sin φ))
4. Apply chirp postmultiplication (same chirp as step 2).
5. 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.

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Notes

• 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.

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License

MIT