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

`class vDSP.DFT`

A single- and double-precision discrete Fourier transform.

`enum vDSP.DFTTransformType`

Discrete Fourier transform types.

Discrete Fourier Transforms

The functions in the Discrete Fourier Transforms (DFT) family calculate a discrete Fourier transform of a specified length on a vector.

`func vDSP_DFT_zop_CreateSetupD(vDSP_DFT_SetupD?, vDSP_Length, vDSP_DFT_Direction) -> vDSP_DFT_SetupD?`

Creates a data structure for use with `vDSP_DFT_ExecuteD(_:_:_:_:_:)` to perform a double-precision, complex-to-complex discrete Fourier transform, forward or inverse.

`func vDSP_DFT_zrop_CreateSetup(vDSP_DFT_Setup?, vDSP_Length, vDSP_DFT_Direction) -> vDSP_DFT_Setup?`

Creates a data structure for use with `vDSP_DFT_Execute(_:_:_:_:_:)` to perform a single-precision discrete Fourier transform, forward (real to complex) or inverse (complex to real).

`func vDSP_DFT_zrop_CreateSetupD(vDSP_DFT_SetupD?, vDSP_Length, vDSP_DFT_Direction) -> vDSP_DFT_SetupD?`

Creates a data structure for use with `vDSP_DFT_ExecuteD(_:_:_:_:_:)` to perform a double-precision discrete Fourier transform, forward (real to complex) or inverse (complex to real).

`func vDSP_DFT_DestroySetup(vDSP_DFT_Setup?)`

Releases a single-precision setup object.

`func vDSP_DFT_DestroySetupD(vDSP_DFT_SetupD?)`

Releases a double-precision setup object.

Data Types

`typealias vDSP_DFT_Setup`

An opaque type that contains setup information for a given DFT transform.

Constants

`enum vDSP_DFT_Direction`

Specifies whether to perform a forward or inverse DFT.

Fourier and Cosine Transforms

Finding the Component Frequencies in a Composite Sine Wave

Use 1D fast Fourier transform to compute the frequency components of a signal.

Using Windowing with Discrete Fourier Transforms

Multiply signal data by window sequence values to reduce spectral leakage.

Signal Extraction from Noise

Use Accelerate’s discrete cosine transform to remove noise from a signal.

Halftone Descreening with 2D Fast Fourier Transform

Reduce or remove periodic artifacts from images.

Fast Fourier Transforms

Transform vectors and matrices of temporal and spatial domain complex values to the frequency domain and vice versa.

Discrete Cosine Transforms

Transform vectors of temporal and spatial domain real values to the frequency domain and vice versa.