---
title: "HermiteanToRealFFT(_:axes:descriptor:name:)"
framework: metalperformanceshadersgraph
role: symbol
role_heading: Instance Method
path: "metalperformanceshadersgraph/mpsgraph/hermiteantorealfft(_:axes:descriptor:name:)"
---

# HermiteanToRealFFT(_:axes:descriptor:name:)

Creates a Hermitean-to-real fast Fourier transform operation and returns the result tensor.

## Declaration

```swift
func HermiteanToRealFFT(_ tensor: MPSGraphTensor, axes: [NSNumber], descriptor: MPSGraphFFTDescriptor, name: String?) -> MPSGraphTensor
```

## Parameters

- `tensor`: A complex-valued input tensor with reduced size (see Discussion). Must have datatype MPSDataTypeComplexFloat32, MPSDataTypeComplexFloat16 or MPSDataTypeComplexBFloat16.
- `axes`: An array of numbers that specifies over which axes MPSGraph performs the Fourier transform - all axes must be contained within last four dimensions of the input tensor.
- `descriptor`: A descriptor that defines the parameters of the Fourier transform operation - see doc://com.apple.metalperformanceshadersgraph/documentation/MetalPerformanceShadersGraph/MPSGraphFFTDescriptor.
- `name`: The name for the operation.

## Return Value

Return Value A valid MPSGraphTensor of type MPSDataTypeFloat32, MPSDataTypeFloat16 or MPSDataTypeBFloat16 (full size).

## Discussion

Discussion This operation computes the fast Fourier transform of a complex-valued input tensor according to the following formulae.     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), + 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 = YES and x = 0 otherwise. tip: Currently transformation is supported 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 transpose(_:permutation:name:)  to be within that last four and then transpose the result tensor back with the inverse of the input transpose.