Module_Extensions_FFTW

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FFTW extension

Vorcyc.Mathematics.Extensions.FFTW is a standalone NuGet package that provides a .NET wrapper around the FFTW (Fastest Fourier Transform in the West) native library. The extension depends on the main library Vorcyc.Mathematics and uses its PinnableArray<T>, ComplexFp32, Complex<T>, and related types for efficient memory pinning and complex arithmetic.

Assembly name: Vorcyc.Mathematics.Extensions.FFTW
Namespace: Vorcyc.Mathematics.Extensions.FFTW
Package version: 0.10.20 (aligned with Vorcyc.Mathematics; no FFTW API change)
Dependencies: Vorcyc.Mathematics (main library) + FFTW native DLL (shipped with the package under runtimes/win-x64/native)

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📒Contents

• 🔖 Single-precision DFT
  • 🔖 Dft1D — 1D transform
  • 🔖 Dft2D — 2D transform
  • 🔖 Dft3D — 3D transform
  • 🔖 DftND — N-dimensional transform
  • 🔖 RealToRealTransforms — real-to-real transforms
  • 🔖 Utilities — utility methods
• 🔖 Double-precision DFT
  • 🔖 Dft1D — 1D transform (double precision)
  • 🔖 Dft2D — 2D transform (double precision)
  • 🔖 Dft3D — 3D transform (double precision)
  • 🔖 DftND — N-dimensional transform (double precision)
  • 🔖 RealToRealTransforms — real-to-real transforms (double precision)
  • 🔖 Utilities — utility methods (double precision)
• 🔖 HilbertTransform class
• 🔖 EnvelopeComputer class
• 🔖 SignalExtension class
• 🔖 PinnableArraySignalExtension class

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Single-precision DFT

The following classes are static (partial) classes in namespace Vorcyc.Mathematics.Extensions.FFTW. Input/output uses ComplexFp32 (single-precision complex) or float.

Dft1D — 1D transform

Provides static methods for one-dimensional discrete Fourier transforms, wrapping the FFTW single-precision interface.

Method	Description
Forward(...)	Complex-to-complex forward DFT (non-in-place)
Inverse(...)	Complex-to-complex inverse DFT (non-in-place)
ForwardInPlace(...)	Complex-to-complex forward DFT (in-place)
InverseInPlace(...)	Complex-to-complex inverse DFT (in-place)
Forward(ReadOnlySpan<float>, ...)	Real-to-complex (R2C) forward DFT
Inverse(..., Span<float>, ...)	Complex-to-real (C2R) inverse DFT

Each method provides overloads for PinnableArray<T>, Span<T>, and raw pointers.

Note: FFTW does not normalize by default; inverse transforms typically require scaling by 1/N. C2R overloads provide an optional scale parameter.

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Dft2D — 2D transform

Provides forward and inverse two-dimensional complex-to-complex (C2C) DFT.

Method	Description
Forward(input, output, nx, ny, ...)	2D C2C forward DFT
Inverse(input, output, nx, ny, ...)	2D C2C inverse DFT

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Dft3D — 3D transform

Provides forward and inverse three-dimensional complex-to-complex (C2C) DFT.

Method	Description
Forward(input, output, nx, ny, nz, ...)	3D C2C forward DFT
Inverse(input, output, nx, ny, nz, ...)	3D C2C inverse DFT

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DftND — N-dimensional transform

Provides C2C, R2C, and C2R transforms of arbitrary dimensionality.

Method	Description
Forward(input, output, dims, ...)	N-dimensional C2C forward DFT
Inverse(input, output, dims, ...)	N-dimensional C2C inverse DFT
Forward(ReadOnlySpan<float>, ..., dims)	N-dimensional R2C forward DFT
Inverse(..., Span<float>, dims, ...)	N-dimensional C2R inverse DFT

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RealToRealTransforms — real-to-real transforms (single precision)

Real-to-real (R2R) transforms based on FFTW fftw_kind, supporting 1D / 2D / 3D / N-D.

Method	Description
R2HC1D(...)	1D real-to-half-complex spectrum
HC2R1D(...)	1D half-complex spectrum to real
DHT1D(...)	1D discrete Hartley transform
R2R_2D(...)	2D R2R transform
R2R_3D(...)	3D R2R transform
R2R_ND(...)	N-dimensional R2R transform

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Utilities — utility methods (single precision)

Method	Description
EstimateFlops(...)	Estimates floating-point operations for a 1D C2C DFT (adds, muls, fmas)
PrintPlan(...)	Prints a human-readable description of an FFTW plan

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Double-precision DFT

Structurally identical to the single-precision version, using Complex<double> or double types. All classes are partial and share class names with the single-precision classes (organized across partial files).

Dft1D — 1D transform (double precision)

Double-precision 1D C2C, R2C, and C2R transforms; API is symmetric with the single-precision version.

Dft2D — 2D transform (double precision)

Double-precision 2D C2C transforms.

Dft3D — 3D transform (double precision)

Double-precision 3D C2C transforms.

DftND — N-dimensional transform (double precision)

Double-precision C2C, R2C, and C2R transforms of arbitrary dimensionality.

RealToRealTransforms — real-to-real transforms (double precision)

Double-precision R2R transforms (1D / 2D / 3D / N-D); API is symmetric with the single-precision version.

Utilities — utility methods (double precision)

Double-precision FLOPs estimation and plan printing utilities.

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HilbertTransform class

Computes the Hilbert transform of real-valued signals using FFT-based analytic signal construction. Commonly used to form analytic signals, extract instantaneous phase and amplitude, or perform envelope detection.

Method	Description
ComputeHilbertTransform(ReadOnlySpan<float>)	Computes the Hilbert transform of a single-precision real-valued signal
ComputeHilbertTransform(ReadOnlySpan<double>)	Computes the Hilbert transform of a double-precision real-valued signal

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EnvelopeComputer class

Computes signal envelopes using the Hilbert transform and peak detection.

LowerEnvelopeMode enum

Value	Description
Symmetric	Lower envelope is the negation of the upper envelope (assumes signal oscillates symmetrically around zero)
Independent	Lower envelope is computed independently (negate the signal first, then apply the Hilbert transform)

Method	Description
ComputeHilbertEnvelope(...)	Computes upper/lower envelopes of a signal

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SignalExtension class

Provides FFTW-based frequency-domain transform extension methods for the standard SignalProcessing.Signals APIs (Signal, SignalSegment, ModifiableTimeDomainSignal). Because FFTW supports DFT of arbitrary length, signals do not need to be zero-padded to a power of two.

Extension target	Method	Description
Signal	TransformToFrequencyDomainFFTW(WindowType?)	Transforms a signal to the frequency domain, with optional window function
SignalSegment	TransformToFrequencyDomainFFTW(WindowType?)	Transforms a signal segment to the frequency domain
ModifiableTimeDomainSignal	TransformToFrequencyDomainFFTW(WindowType?)	Transforms a modifiable signal to the frequency domain

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PinnableArraySignalExtension class

Provides signal/spectrum-related extension methods for PinnableArray<float> and PinnableArray<double>.

Extension target	Method	Description
PinnableArray<float>	ScaleInPlace()	Scales in place by 1/N (for inverse FFT normalization)
PinnableArray<double>	ScaleInPlace()	Scales in place by 1/N (double-precision version)

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