fft2 — Compute the two-dimensional discrete Fourier transform (DFT) of numeric or complex data.

fft2(X) computes the two-dimensional discrete Fourier transform (DFT) of X. It is equivalent to applying fft along the first dimension and then along the second dimension, preserving MATLAB’s column-major ordering and output shape semantics.

How fft2 works

• fft2(X) transforms along the first and second dimensions that have size greater than one.
• fft2(X, M, N) zero-pads or truncates X to M rows and N columns before evaluating the 2-D transform.
• fft2(X, SIZE) accepts a two-element vector (or scalar) specifying the transform lengths.
• Real inputs produce complex outputs; complex inputs are transformed element-wise with no additional conversion.
• Higher-dimensional inputs are transformed slice-by-slice across trailing dimensions, matching MATLAB behaviour.
• Empty dimensions yield empty outputs; zero padding with 0 produces a zero-sized complex tensor.
• GPU arrays execute on-device when the provider advertises the fft_dim hook; otherwise RunMat gathers the data and performs the transform on the host using rustfft.

GPU memory and residency

You usually do NOT need to call gpuArray manually. The fusion planner and native acceleration layer keep tensors on the GPU when a provider offers FFT kernels. If the provider lacks fft_dim, RunMat gathers inputs, evaluates the FFT pair on the host, and returns a MATLAB-compatible complex tensor. You can still use gpuArray for explicit residency control, particularly when interoperating with MATLAB code that expects it.

Examples

Computing the 2-D FFT of a small matrix

X = [1 2; 3 4];
Y = fft2(X)

Expected output:

Y =
    10 + 0i   -2 + 0i
    -4 + 0i    0 + 0i

Zero-padding an image patch before fft2

patch = [1 0 1; 0 1 0; 1 0 1];
F = fft2(patch, 8, 8)

Specifying transform lengths with a size vector

X = rand(4, 6);
F = fft2(X, [8 4]);   % pad rows to 8 and truncate columns to 4

Using fft2 on gpuArray data

G = gpuArray(rand(256, 256));
F = fft2(G);
R = gather(F)

Applying fft2 to each slice of a 3-D volume

V = rand(64, 64, 10);
spectra = fft2(V)

Verifying fft2 against sequential fft calls

X = rand(5, 7);
sequential = fft(fft(X, [], 1), [], 2);
direct = fft2(X)

FAQ

Related Math functions

Open-source implementation

Unlike proprietary runtimes, every RunMat function is open-source. Read exactly how fft2 works, line by line, in Rust.

• View fft2.rs on GitHub
• Learn how the runtime works
• Found a bug? Open an issue with a minimal reproduction.

About RunMat

RunMat is an open-source runtime that executes MATLAB-syntax code — faster, on any GPU, with no license required.

• Simulations that took hours now take minutes. RunMat automatically optimizes your math for GPU execution on Apple, Nvidia, and AMD hardware. No code changes needed.
• Start running code in seconds. Open the browser sandbox or download a single binary. No license server, no IT ticket, no setup.
• A full development environment. GPU-accelerated 2D and 3D plotting, automatic versioning on every save, and a browser IDE you can share with a link.

Getting started · Benchmarks · Pricing