# Discrete Fourier transforms Transform vectors of temporal and spatial domain complex values to the frequency domain, and vice versa. ## Topics ### Objects that simplify discrete Fourier transforms [`DiscreteFourierTransform`](/documentation/Accelerate/vDSP/DiscreteFourierTransform) An object that provides forward and inverse discrete Fourier transforms on single- or double-precision collections of interleaved or split-complex data. [`DFTTransformType`](/documentation/Accelerate/vDSP/DFTTransformType) Discrete Fourier transform types. [`DFT`](/documentation/Accelerate/vDSP/DFT) A single- and double-precision discrete Fourier transform. ### Interleaved discrete Fourier transform functions [`vDSP_DFT_Interleaved_CreateSetup`](/documentation/Accelerate/vDSP_DFT_Interleaved_CreateSetup(_:_:_:_:)) Returns a setup structure that contains precalculated data for forward and inverse, single-precision interleaved discrete Fourier transform (DFT) functions. [`vDSP_DFT_Interleaved_CreateSetupD`](/documentation/Accelerate/vDSP_DFT_Interleaved_CreateSetupD(_:_:_:_:)) Returns a setup structure that contains precalculated data for forward and inverse, double-precision interleaved discrete Fourier transform (DFT) functions. [`vDSP_DFT_Interleaved_Execute`](/documentation/Accelerate/vDSP_DFT_Interleaved_Execute(_:_:_:)) Calculates the single-precision discrete Fourier transform (DFT) for a vector of interleaved complex values. [`vDSP_DFT_Interleaved_ExecuteD`](/documentation/Accelerate/vDSP_DFT_Interleaved_ExecuteD(_:_:_:)) Calculates the double-precision discrete Fourier transform (DFT) for a vector of interleaved complex values. [`vDSP_DFT_Interleaved_DestroySetup`](/documentation/Accelerate/vDSP_DFT_Interleaved_DestroySetup(_:)) Releases a single-precision discrete Fourier transform (DFT) setup structure. [`vDSP_DFT_Interleaved_DestroySetupD`](/documentation/Accelerate/vDSP_DFT_Interleaved_DestroySetupD(_:)) Releases a double-precision discrete Fourier transform (DFT) setup structure. ### Real discrete Fourier transform setup [`vDSP_DFT_zrop_CreateSetup`](/documentation/Accelerate/vDSP_DFT_zrop_CreateSetup) Returns a setup structure that contains precalculated data for forward and inverse, real, single-precision DFT functions. [`vDSP_DFT_zrop_CreateSetupD`](/documentation/Accelerate/vDSP_DFT_zrop_CreateSetupD) Returns a setup structure that contains precalculated data for forward and inverse, real, double-precision DFT functions. ### Complex discrete Fourier transform setup [`vDSP_DFT_zop_CreateSetup`](/documentation/Accelerate/vDSP_DFT_zop_CreateSetup) Returns a setup structure that contains precalculated data for forward and inverse, complex, single-precision DFT functions. [`vDSP_DFT_zop_CreateSetupD`](/documentation/Accelerate/vDSP_DFT_zop_CreateSetupD) Returns a setup structure that contains precalculated data for forward and inverse, complex, double-precision DFT functions. ### Functions to perform discrete Fourier transforms [`vDSP_DFT_Execute`](/documentation/Accelerate/vDSP_DFT_Execute) Calculates the discrete single-precision Fourier transform for a vector. [`vDSP_DFT_ExecuteD`](/documentation/Accelerate/vDSP_DFT_ExecuteD) Calculates the discrete double-precision Fourier transform for a vector. ### Discrete Fourier transform cleanup [`vDSP_DFT_DestroySetup`](/documentation/Accelerate/vDSP_DFT_DestroySetup) Releases a single-precision setup structure. [`vDSP_DFT_DestroySetupD`](/documentation/Accelerate/vDSP_DFT_DestroySetupD) Releases a double-precision setup structure. ### Data types [`vDSP_DFT_Interleaved_Setup`](/documentation/Accelerate/vDSP_DFT_Interleaved_Setup) An opaque type that contains setup information for an interleaved single-precision discrete Fourier transform (DFT). [`vDSP_DFT_Interleaved_SetupD`](/documentation/Accelerate/vDSP_DFT_Interleaved_SetupD) An opaque type that contains setup information for an interleaved double-precision discrete Fourier transform (DFT). [`vDSP_DFT_Setup`](/documentation/Accelerate/vDSP_DFT_Setup) An opaque type that contains setup information for a single-precision discrete Fourier transform (DFT). [`vDSP_DFT_SetupD`](/documentation/Accelerate/vDSP_DFT_SetupD) An opaque type that contains setup information for a double-precision discrete Fourier transform (DFT). ### Constants [`vDSP_DFT_Direction`](/documentation/Accelerate/vDSP_DFT_Direction) An enumeration that specifies whether to perform a forward or inverse DFT. ### Enumerations [`vDSP_DFT_RealtoComplex`](/documentation/Accelerate/vDSP_DFT_RealtoComplex) --- 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)