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

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

Creates a fast Fourier transform operation and returns the result tensor.

## Declaration

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

## Parameters

- `tensor`: A complex or real-valued input tensor.
- `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 complex-valued MPSGraphTensor of the same shape as tensor.

## Discussion

Discussion This operation computes the fast Fourier transform of the input tensor according to the following formulae.     output[mu] = scale * sum_nu exp( +/- i * 2Pi * mu * nu / n ) input[nu], where 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. 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 transpose(_:permutation:name:)  to be within that last four and then transpose the result tensor back with the inverse of the input transpose.