# HermiteanToRealFFT(_:axesTensor:descriptor:name:) Creates a Hermitean-to-real fast Fourier transform operation and returns the result tensor. ``` func HermiteanToRealFFT(_ tensor: MPSGraphTensor, axesTensor: MPSGraphTensor, descriptor: MPSGraphFFTDescriptor, name: String?) -> MPSGraphTensor ``` ## Parameters `tensor` A complex-valued input tensor with reduced size (see Discussion). Must have datatype `MPSDataTypeComplexFloat32`, `MPSDataTypeComplexFloat16` or `MPSDataTypeComplexBFloat16`. `axesTensor` A tensor of rank one containing the axes over which MPSGraph performs the transformation. See [`fastFourierTransform(_:axes:descriptor:name:)`](/documentation/MetalPerformanceShadersGraph/MPSGraph/fastFourierTransform(_:axes:descriptor:name:)). `descriptor` A descriptor that defines the parameters of the Fourier transform operation - see [`MPSGraphFFTDescriptor`](/documentation/MetalPerformanceShadersGraph/MPSGraphFFTDescriptor). `name` The name for the operation. ## Return Value A valid MPSGraphTensor of type `MPSDataTypeFloat32`, `MPSDataTypeFloat16` or `MPSDataTypeBFloat16` (full size). ## Discussion This operation computes the fast Fourier transform of a complex-valued input tensor according to the following formulae. ```md output[mu] = scale * sum_nu exp( +/- i * 2Pi * mu * nu / n ) in'[nu], where ``` `in'[nu] = conjugate(in[n - nu])`, for the last dimension defined by `axes` when `nu` is out of range of the input dimension. `scale = 1` for `scaling_mode = none`, `scale = 1/V_f` for `scaling_mode = size`, `scale = 1/sqrt(V_f)` for `scaling_mode = unitary`, where `V_f` is the volume of the transformation defined by the dimensions included in `axes` (`V_f = prod_{i \in axes} shape(input)[i]`) (see [`scalingMode`](/documentation/MetalPerformanceShadersGraph/MPSGraphFFTDescriptor/scalingMode)), `+` is selected in `+/-` when `inverse` is specified, otherwise `-` is used and the sum is done separately over each dimension in `axes` and `n` is the dimension length of that axis. With this API MPSGraph treats the input tensor to have only the unique frequencies, which means that the resulting tensor has size `(inSize-1)*2 + x` in the last dimension defined by `axes`, where `inSize = shape(input)[axis] ( = (n/2)+1 )` is the size of the input `tensor` in the last transformed dimension and `x = 1` when [`roundToOddHermitean`](/documentation/MetalPerformanceShadersGraph/MPSGraphFFTDescriptor/roundToOddHermitean) = `YES` and `x = 0` otherwise. > Tip: Currently MPSGraph supports the transformation only within the last four dimensions of the input tensor. In case > you need to transform higher dimensions than the last four, you can tranpose the higher dimensions of the input > with ``doc://com.apple.metalperformanceshadersgraph/documentation/MetalPerformanceShadersGraph/MPSGraph/transpose(_:permutation:name:)`` to be within that last four and then transpose > the result tensor back with the inverse of the input transpose. --- Copyright © 2026 Apple Inc. All rights reserved. | [Terms of Use](https://www.apple.com/legal/internet-services/terms/site.html) | [Privacy Policy](https://www.apple.com/privacy/privacy-policy)