`fft2` — Compute two-dimensional discrete Fourier transforms in MATLAB and RunMat.

fft2(X) computes the two-dimensional discrete Fourier transform of X. It is equivalent to applying fft along the first two dimensions, with shape and ordering behavior consistent with MATLAB and RunMat.

Syntax

Y = fft2(X)
Y = fft2(X, SIZE)
Y = fft2(X, M, N)

Inputs

Name	Type	Required	Default	Description
`X`	`Any`	Yes	—	Input array.
`SIZE`	`NumericArray`	No	—	RunMat-only scalar N or two-element [M N] size shorthand.
`M`	`NumericScalar`	No	—	Positive output row count for transform.
`N`	`NumericScalar`	No	—	Positive output column count for transform.

Returns

Name	Type	Description
`Y`	`NumericArray`	2-D complex Fourier spectrum output.

Errors

Identifier	When	Message
`RunMat:fft2:ArgCount`	More than three input arguments are supplied.	`fft2: invalid argument count`
`RunMat:fft2:InvalidLength`	Length/size arguments are invalid.	`fft2: invalid transform length argument`
`RunMat:fft2:InvalidSizeVector`	Single SIZE argument is invalid.	`fft2: invalid size vector argument`
`RunMat:fft2:InvalidInput`	Input cannot be converted to supported numeric/complex domain.	`fft2: invalid input`
`RunMat:fft2:Internal`	FFT2 execution or tensor shaping fails.	`fft2: internal error`

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.
RunMat extension: fft2(X, SIZE) accepts a two-element vector (or scalar) specifying the transform lengths when RunMat extensions are enabled.
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.
MATLAB-compatible M and N controls are positive integer scalars. Empty and zero transform sizes are separately gated RunMat extensions.
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]);   % requires RunMat extension mode

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)

Using `fft2` with coding agents

Open a RunMat example with live inputs, then ask the agent to explain how fft2 changes the result.

Run a small fft2 example, explain the result, then change one input and compare the output.

FAQ

Is fft2(X) the same as fft(fft(X, [], 1), [], 2)?⌄

Yes. RunMat literally performs the two sequential transforms so the results match MATLAB exactly.

How do zero-length transform sizes behave?⌄

MATLAB-compatible mode requires positive M and N. RunMat extension mode can use 0 to produce a zero-sized complex tensor.

Can I use a single scalar for the size argument?⌄

In RunMat extension mode, fft2(X, K) is shorthand for fft2(X, [K K]). The documented compatibility forms are fft2(X) and fft2(X,M,N).

What happens when X has more than two dimensions?⌄

RunMat applies fft2 to every 2-D slice defined by the first two dimensions, leaving higher dimensions untouched.

Do I get complex outputs for real inputs?⌄

Always. Even when the imaginary parts are zero, outputs are stored as complex tensors to mirror MATLAB semantics.

Will fft2 run on the GPU automatically?⌄

Yes if the input's owning provider implements fft_dim for its storage class. Otherwise RunMat gathers to the host, performs the transform with rustfft, and restores the result to that provider.

Does fft2 normalise the output?⌄

No. Like MATLAB, the forward FFT leaves scaling untouched; use ifft2 for the inverse with 1/(M*N) scaling.

Can I mix [] with explicit sizes (e.g., fft2(X, [], 128))?⌄

This is a RunMat extension. MATLAB-compatible mode requires positive scalar M and N values.

Open-source implementation

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

View the source for fft2 in Rust on GitHub
Learn how the RunMat 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 blazing on any GPU. It is licensed under the Apache 2.0 license.

RunMat automatically optimizes your math for GPU execution on Apple, Nvidia, and AMD hardware. No code changes needed. Simulations that took hours now take minutes.
Start running code in seconds. RunMat runs in the browser, on the desktop, or from the CLI. No license server, no IT ticket.

Getting started · Benchmarks · Pricing

`fft2` — Compute two-dimensional discrete Fourier transforms in MATLAB and RunMat.

Syntax

Y = fft2(X)
Y = fft2(X, SIZE)
Y = fft2(X, M, N)

Inputs

Name	Type	Required	Default	Description
`X`	`Any`	Yes	—	Input array.
`SIZE`	`NumericArray`	No	—	RunMat-only scalar N or two-element [M N] size shorthand.
`M`	`NumericScalar`	No	—	Positive output row count for transform.
`N`	`NumericScalar`	No	—	Positive output column count for transform.

Returns

Name	Type	Description
`Y`	`NumericArray`	2-D complex Fourier spectrum output.

Errors

Identifier	When	Message
`RunMat:fft2:ArgCount`	More than three input arguments are supplied.	`fft2: invalid argument count`
`RunMat:fft2:InvalidLength`	Length/size arguments are invalid.	`fft2: invalid transform length argument`
`RunMat:fft2:InvalidSizeVector`	Single SIZE argument is invalid.	`fft2: invalid size vector argument`
`RunMat:fft2:InvalidInput`	Input cannot be converted to supported numeric/complex domain.	`fft2: invalid input`
`RunMat:fft2:Internal`	FFT2 execution or tensor shaping fails.	`fft2: internal error`

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.
RunMat extension: fft2(X, SIZE) accepts a two-element vector (or scalar) specifying the transform lengths when RunMat extensions are enabled.
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.
MATLAB-compatible M and N controls are positive integer scalars. Empty and zero transform sizes are separately gated RunMat extensions.
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

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]);   % requires RunMat extension mode

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)

Using `fft2` with coding agents

Open a RunMat example with live inputs, then ask the agent to explain how fft2 changes the result.

Run a small fft2 example, explain the result, then change one input and compare the output.

FAQ

Is fft2(X) the same as fft(fft(X, [], 1), [], 2)?⌄

Yes. RunMat literally performs the two sequential transforms so the results match MATLAB exactly.

How do zero-length transform sizes behave?⌄

MATLAB-compatible mode requires positive M and N. RunMat extension mode can use 0 to produce a zero-sized complex tensor.

Can I use a single scalar for the size argument?⌄

In RunMat extension mode, fft2(X, K) is shorthand for fft2(X, [K K]). The documented compatibility forms are fft2(X) and fft2(X,M,N).

What happens when X has more than two dimensions?⌄

RunMat applies fft2 to every 2-D slice defined by the first two dimensions, leaving higher dimensions untouched.

Do I get complex outputs for real inputs?⌄

Always. Even when the imaginary parts are zero, outputs are stored as complex tensors to mirror MATLAB semantics.

Will fft2 run on the GPU automatically?⌄

Yes if the input's owning provider implements fft_dim for its storage class. Otherwise RunMat gathers to the host, performs the transform with rustfft, and restores the result to that provider.

Does fft2 normalise the output?⌄

No. Like MATLAB, the forward FFT leaves scaling untouched; use ifft2 for the inverse with 1/(M*N) scaling.

Can I mix [] with explicit sizes (e.g., fft2(X, [], 128))?⌄

This is a RunMat extension. MATLAB-compatible mode requires positive scalar M and N values.

Fft

fft · fftn · fftshift · ifft · ifft2 · ifftn · ifftshift

Elementwise

Trigonometry

acos · acosh · asin · asinh · atan · atan2 · atanh · cos · cosd · cosh · cospi · deg2rad · pol2cart · rad2deg · sin · sind · sinh · sinpi · tan · tand · tanh

Reduction

Structure

bandwidth · isdiag · ishermitian · issymmetric · istril · istriu · symrcm

Signal

Rounding

ceil · fix · floor · mod · rem · round

Factor

chol · decomposition · eig · eigs · lu · qr · svd

Solve

cond · det · inv · linsolve · norm · null · pinv · rank · rcond · rref · vecnorm

Optim

coneprog · fminbnd · fminunc · fsolve · fzero · integral · linprog · lsqcurvefit · lsqnonlin · optimoptions · optimset · quad · secondordercone

Ops

cross · ctranspose · dot · mldivide · mpower · mrdivide · mtimes · pagemtimes · pagetranspose · trace · transpose

Symbolic

digits · int · limit · piecewise · sym · syms · vpa

Interpolation

griddedInterpolant · interp1 · interp1q · interp2 · pchip · ppval · spline

Discrete

lcm · primes

Ode

ode15s · ode23 · ode45

Poly

polyder · polyfit · polyint · polyval · roots

Open-source implementation

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

View the source for fft2 in Rust on GitHub
Learn how the RunMat 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 blazing on any GPU. It is licensed under the Apache 2.0 license.

RunMat automatically optimizes your math for GPU execution on Apple, Nvidia, and AMD hardware. No code changes needed. Simulations that took hours now take minutes.
Start running code in seconds. RunMat runs in the browser, on the desktop, or from the CLI. No license server, no IT ticket.

Getting started · Benchmarks · Pricing

fft2 — Compute two-dimensional discrete Fourier transforms in MATLAB and RunMat.

Syntax

Inputs

Returns

Errors

How fft2 works

GPU memory and residency

Examples

Computing the 2-D FFT of a small matrix

Zero-padding an image patch before fft2

Specifying transform lengths with a size vector

Using fft2 on gpuArray data

Applying fft2 to each slice of a 3-D volume

Verifying fft2 against sequential fft calls

Using fft2 with coding agents

FAQ

Related Math functions

Fft

Elementwise

Trigonometry

Reduction

Structure

Signal

Rounding

Factor

Solve

Optim

Ops

Symbolic

Interpolation

Discrete

Ode

Poly

Open-source implementation

About RunMat

Download RunMat

fft2 — Compute two-dimensional discrete Fourier transforms in MATLAB and RunMat.

Syntax

Inputs

Returns

Errors

How fft2 works

GPU memory and residency

Examples

Computing the 2-D FFT of a small matrix

Zero-padding an image patch before fft2

Specifying transform lengths with a size vector

Using fft2 on gpuArray data

Applying fft2 to each slice of a 3-D volume

Verifying fft2 against sequential fft calls

Using fft2 with coding agents

FAQ

Related Math functions

Fft

Elementwise

Trigonometry

Reduction

Structure

Signal

Rounding

Factor

Solve

Optim

Ops

Symbolic

Interpolation

Discrete

Ode

Poly

Open-source implementation

About RunMat

Download RunMat

`fft2` — Compute two-dimensional discrete Fourier transforms in MATLAB and RunMat.

How `fft2` works

Zero-padding an image patch before `fft2`

Using `fft2` on `gpuArray` data

Applying `fft2` to each slice of a 3-D volume

Verifying `fft2` against sequential `fft` calls

Using `fft2` with coding agents

`fft2` — Compute two-dimensional discrete Fourier transforms in MATLAB and RunMat.

How `fft2` works

Zero-padding an image patch before `fft2`

Using `fft2` on `gpuArray` data

Applying `fft2` to each slice of a 3-D volume

Verifying `fft2` against sequential `fft` calls

Using `fft2` with coding agents