# vDSP.DiscreteFourierTransform An object that provides forward and inverse discrete Fourier transforms on single- or double-precision collections of interleaved or split-complex data. ``` class DiscreteFourierTransform where T : vDSP_DiscreteFourierTransformable ``` ## Overview Use a [`vDSP.DiscreteFourierTransform`](/documentation/Accelerate/vDSP/DiscreteFourierTransform) to perform discrete Fourier transforms (DFTs) on split-complex or interleaved data. To learn more about working with split-complex and interleaved data, see . To create a [`vDSP.DiscreteFourierTransform`](/documentation/Accelerate/vDSP/DiscreteFourierTransform) instance to work with interleaved data, pass either [`DSPComplex`](/documentation/Accelerate/DSPComplex) or [`DSPDoubleComplex`](/documentation/Accelerate/DSPDoubleComplex) to [`init(previous:count:direction:transformType:ofType:)`](/documentation/Accelerate/vDSP/DiscreteFourierTransform/init(previous:count:direction:transformType:ofType:)). The following code shows how to perform a forward complex-to-complex DFT on the interleaved single-precision values in the `interleavedInput` array: ```swift // The `interleavedInput` array contains `complexValuesCount` `DSPComplex` elements. let interleavedInput: [DSPComplex] = [ ... ] let interleavedDFT = try? vDSP.DiscreteFourierTransform(previous: nil, count: complexValuesCount, direction: .forward, transformType: .complexComplex, ofType: DSPComplex.self) // On return, the `interleavedOutput` array contains an array of `DSPComplex` // structures. let interleavedOutput = interleavedDFT?.transform(input: interleavedInput) ``` To create a [`vDSP.DiscreteFourierTransform`](/documentation/Accelerate/vDSP/DiscreteFourierTransform) instance to work with split-complex data, pass either or to [`init(previous:count:direction:transformType:ofType:)`](/documentation/Accelerate/vDSP/DiscreteFourierTransform/init(previous:count:direction:transformType:ofType:)). Split-complex data stores the real and imaginary parts of each complex value in separate arrays. The following code shows how to perform forward complex-to-complex DFT on the split-complex single-precision values in the `splitComplexRealInput` and `splitComplexImaginaryInput` arrays: ```swift var splitComplexRealInput: [Float] = [ ... ] var splitComplexImaginaryInput: [Float] = [ ... ] let splitComplexDFT = try? vDSP.DiscreteFourierTransform(previous: nil, count: complexValuesCount, direction: .forward, transformType: .complexComplex, ofType: Float.self) // The `splitComplexOutput` tuple contains two arrays that represent the // real and imaginary parts of the output. let splitComplexOutput = splitComplexDFT?.transform(real: splitComplexRealInput, imaginary: splitComplexImaginaryInput) ``` If the underlying data in both the `interleavedInput` array and the split-complex input arrays is the same, for each `i` in `0 ..< complexValuesCount`, the following is true`:` ```c interleavedOutput[i].real ≈ splitComplexOutput.real[i] interleavedOutput[i].imag ≈ splitComplexOutput.imaginary[i] ``` `` ## Topics ### Creating a Discrete Fourier Transform Instance [`init(previous:count:direction:transformType:ofType:)`](/documentation/Accelerate/vDSP/DiscreteFourierTransform/init(previous:count:direction:transformType:ofType:)) Returns a new discrete Fourier transform instance. ### Performing Split-Complex Discrete Fourier Transforms [`transform(real:imaginary:)`](/documentation/Accelerate/vDSP/DiscreteFourierTransform/transform(real:imaginary:)-4nwy9) Returns the result of a single-precision discrete Fourier transform. [`transform(real:imaginary:)`](/documentation/Accelerate/vDSP/DiscreteFourierTransform/transform(real:imaginary:)-82jag) Returns the result of a double-precision discrete Fourier transform. [`transform(inputReal:inputImaginary:outputReal:outputImaginary:)`](/documentation/Accelerate/vDSP/DiscreteFourierTransform/transform(inputReal:inputImaginary:outputReal:outputImaginary:)-sihh) Computes a single-precision discrete Fourier transform. [`transform(inputReal:inputImaginary:outputReal:outputImaginary:)`](/documentation/Accelerate/vDSP/DiscreteFourierTransform/transform(inputReal:inputImaginary:outputReal:outputImaginary:)-7115x) Computes a double-precision discrete Fourier transform. ### Performing Interleaved Discrete Fourier Transforms [`transform(input:)`](/documentation/Accelerate/vDSP/DiscreteFourierTransform/transform(input:)-92b3l) Returns the result of a single-precision discrete Fourier transform. [`transform(input:)`](/documentation/Accelerate/vDSP/DiscreteFourierTransform/transform(input:)-5si4h) Returns the result of a double-precision discrete Fourier transform. [`transform(input:output:)`](/documentation/Accelerate/vDSP/DiscreteFourierTransform/transform(input:output:)-1k3hd) Computes a single-precision discrete Fourier transform. [`transform(input:output:)`](/documentation/Accelerate/vDSP/DiscreteFourierTransform/transform(input:output:)-1tsod) Computes a double-precision discrete Fourier transform. --- 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)