fftshift — Shift zero-frequency components to spectrum centers in MATLAB and RunMat.
fftshift(X) circularly shifts FFT output so the zero-frequency component moves to the center of each shifted dimension. The default all-dimension behavior and optional dimension selection follow MATLAB semantics.
Syntax
Y = fftshift(X)
Y = fftshift(X, DIM)Inputs
| Name | Type | Required | Default | Description |
|---|---|---|---|---|
X | Any | Yes | — | Numeric, complex, logical, or gpuArray input. |
DIM | Any | No | — | Positive scalar dimension; vectors and logical masks are RunMat extensions. |
Returns
| Name | Type | Description |
|---|---|---|
Y | Any | Shifted array with the same size and type family as X. |
Errors
| Identifier | When | Message |
|---|---|---|
RunMat:fftshift:ArgCount | More than two input arguments are supplied. | fftshift: invalid argument count |
RunMat:fftshift:InvalidDimensions | DIM argument is malformed or out of range. | fftshift: invalid dimension argument |
RunMat:fftshift:InvalidInput | X is not a supported numeric/logical input type. | fftshift: expected numeric or logical input |
RunMat:fftshift:UnsupportedInput | X is an unsupported object/cell/function/meta runtime type. | fftshift: unsupported input type |
RunMat:fftshift:Internal | Shifting, tensor reconstruction, or GPU transfer operations fail. | fftshift: internal error |
How fftshift works
- When called without a dimension list,
fftshiftshifts along every dimension byfloor(size(X, dim) / 2). fftshift(X, DIM)shifts one documented scalar dimension. Numeric vectors and logical masks are separately gated RunMat extensions.- Dimensions of length 0 or 1 are left unchanged.
- Inputs can be real or complex and may already reside on the GPU (
gpuArray).
Does RunMat run fftshift on the GPU?
RunMat asks the input's owning provider to execute fftshift via the circshift hook. If the provider cannot satisfy the request, the tensor is gathered once, shifted on the host, and restored to that provider. Scalars remain on their existing device.
GPU memory and residency
RunMat keeps FFT spectra on the GPU whenever the input's owning provider can execute the required circshift. Otherwise RunMat gathers the data once, performs the host shift, and restores the result to the same provider so subsequent work can remain resident. You can call gpuArray explicitly when you want to guarantee a residency boundary.
Examples
Centering the spectrum of a 1-D FFT result with even length
x = [0 1 2 3 4 5 6 7];
fx = fft(x);
y = fftshift(fx)Expected output:
y = [-4 -4-1.6569i -4-4i -4-9.6569i 28 -4+9.6569i -4+4i -4+1.6569i]Handling odd-length vectors
x = 1:5;
y = fftshift(x)Expected output:
y = [4 5 1 2 3]Centering both axes of a 2-D FFT
A = [1 2 3; 4 5 6];
C = fftshift(A)Expected output:
C =
6 4 5
3 1 2Shifting only one dimension of a matrix
A = [1 2 3; 4 5 6];
rowCentered = fftshift(A, 1) % shift rows onlyExpected output:
rowCentered =
4 5 6
1 2 3Applying fftshift to a gpuArray spectrum
G = gpuArray(0:7);
centered = fftshift(G);
H = gather(centered)Expected output:
H = [4 5 6 7 0 1 2 3]Using fftshift with coding agents
Open a RunMat example with live inputs, then ask the agent to explain how fftshift changes the result.
Run a small fftshift example, explain the result, then change one input and compare the output.
FAQ
When should I call fftshift?⌄
Call fftshift whenever you need to center FFT outputs before visualising spectra, computing radial averages, or applying filters that expect zero frequency in the middle of the array.
Does fftshift modify the phase or magnitude of the FFT?⌄
No. fftshift only reorders the samples. Magnitudes, phases, and the overall information content remain unchanged.
How do I undo fftshift?⌄
Use ifftshift, which performs the inverse rearrangement. The sequence ifftshift(fftshift(X)) returns X for all supported inputs.
Can I apply fftshift to only one dimension?⌄
Pass a positive scalar dimension such as fftshift(X,2). RunMat extension mode additionally accepts numeric dimension vectors and logical masks.
Does fftshift work with gpuArray inputs?⌄
Yes. RunMat keeps data on the GPU whenever the provider exposes the circshift hook, matching MATLAB's gpuArray behaviour.
How does fftshift handle empty inputs?⌄
Empty arrays are returned unchanged with identical shape metadata.
Can I use fftshift on logical arrays?⌄
Yes. Logical arrays are shifted without changing their logical element type.
Related Math functions
Elementwise
abs · angle · bsxfun · complex · conj · double · erf · erfcinv · exp · expm1 · factorial · flintmax · gamma · gammaln · heaviside · hypot · idivide · imag · intmax · intmin · ldivide · log · log10 · log1p · log2 · minus · nextpow2 · plus · pow2 · power · rdivide · real · realmax · realmin · realsqrt · rescale · sign · single · sqrt · swapbytes · times · typecast · uint16 · uint32 · uint8
Trigonometry
acos · acosh · asin · asinh · atan · atan2 · atanh · cos · cosd · cosh · cospi · deg2rad · pol2cart · rad2deg · sin · sind · sinh · sinpi · tan · tand · tanh
Reduction
all · any · bounds · cummax · cummin · cumprod · cumsum · cumtrapz · diff · gradient · max · maxk · mean · median · min · mink · movmax · movmean · movmedian · movmin · movprod · movstd · movsum · movvar · nnz · prod · rms · std · sum · trapz · var
Structure
bandwidth · isdiag · ishermitian · issymmetric · istril · istriu · symrcm
Signal
blackman · butter · buttord · cheb2ord · conv · conv2 · deconv · downsample · envelope · filter · filtfilt · fir1 · freqz · gauspuls · hamming · hann · hilbert · periodogram · pulstran · pwelch · rectpuls · resample · sawtooth · sinc · spectrogram · square · tripuls · unwrap · upsample · zplane
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
Open-source implementation
Unlike proprietary runtimes, every RunMat function is open-source. Read exactly how fftshift is executed, line by line, in Rust.
- View the source for fftshift 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.