Fourier Convolve

Collaboration diagram for Fourier Convolve:

Functions
int	ManyConvolveFourier (double Data[], double KernelDht[], double CaS[], double *ScratchBuffer, long SignalLength, double Shift)
int	ManyConvolveFourierSymmetricKernel (double Data[], double KernelDht[], double CaS[], double *ScratchBuffer, long SignalLength, double Shift)
int	OneConvolveFourier (double Data[], double Kernel[], long SignalLength, double Shift, int *Status)
int	OneConvolveFourierSymmetricKernel (double Data[], double SymmetricKernel[], long SignalLength, double Shift, int *Status)

Detailed Description

Function Documentation

ManyConvolveFourier()

int ManyConvolveFourier	(	double	Data[],
		double	KernelDht[],
		double	CaS[],
		double *	ScratchBuffer,
		long	SignalLength,
		double	Shift
	)

Fourier convolution with any kernel. Same conventions as for OneConvolveFourier. Preprocessing steps have to be carrried out elsewhere.

success: return(!ERROR); failure: return(ERROR)

ManyConvolveFourierSymmetricKernel()

int ManyConvolveFourierSymmetricKernel	(	double	Data[],
		double	KernelDht[],
		double	CaS[],
		double *	ScratchBuffer,
		long	SignalLength,
		double	Shift
	)

Fourier convolution with a symmetric kernel. Same conventions as for OneConvolveFourierSymmetricKernel. Preprocessing steps have to be carrried out elsewhere

success: return(!ERROR); failure: return(ERROR)

OneConvolveFourier()

int OneConvolveFourier	(	double	Data[],
		double	Kernel[],
		long	SignalLength,
		double	Shift,
		int *	Status
	)

Fourier convolution 1D. Fourier convolution with any kernel. The kernel has an infinite, periodic (SignalLength) support. The kernel origin (hot spot) is at index [0].

The highest coordinate (SignalLength-2)/2 is at index [(SignalLength-2)/2] for SignalLength even. The highest coordinate (SignalLength-1)/2 is at index [(SignalLength-1)/2] for SignalLength odd.

The lowest coordinate -SignalLength/2 is at index [SignalLength/2] for SignalLength even. The lowest coordinate -(SignalLength-1)/2 is at index [(SignalLength+1)/2] for SignalLength odd.

The coordinate -1 is at index [SignalLength-1] for SignalLength even or odd.

The signal has an infinite, periodic (SignalLength) support. The output has same length SignalLength than the input. The output has already been allocated. The result of the convolution overwrites the input. The inverse DHT of the kernel overwrites the kernel. If the kernel is finite support, don't forget to pad!

success: return(!ERROR); failure: return(ERROR)

The returned value is duplicated in Status

OneConvolveFourierSymmetricKernel()

int OneConvolveFourierSymmetricKernel	(	double	Data[],
		double	SymmetricKernel[],
		long	SignalLength,
		double	Shift,
		int *	Status
	)

Fourier convolution with a symmetrical kernel. The kernel has an infinite, periodic (SignalLength) support. The kernel origin (hot spot) is at index [0]. The highest coordinate (SignalLength-2)/2 is at index [(SignalLength-2)/2] for SignalLength even. For symmetry, kernel[(SignalLength-2)/2] = 0 for SignalLength even.

The highest coordinate (SignalLength-1)/2 is at index [(SignalLength-1)/2] for SignalLength odd. No special symmetry requirement for SignalLength odd.

The lowest coordinate -SignalLength/2 is at index [SignalLength/2] for SignalLength even. The lowest coordinate -(SignalLength-1)/2 is at index [(SignalLength+1)/2] for SignalLength odd.

The coordinate -1 is at index [SignalLength-1] for SignalLength even or odd.

The signal has an infinite, periodic (SignalLength) support. The output has the same length SignalLength than the input. The output has already been allocated.

The kernel is even-symmetric around 0 (k[x] = k[-x]). Only the coord. >= 0 of the kernel need be given.

The result of the convolution overwrites the input. The inverse DHT of the kernel overwrites the kernel. If the kernel is finite support, don't forget to pad!

Observe the separate symmetries for SignalLength odd/even! For a symmetric kernel, DHT <=> DFT

success: return(!ERROR); failure: return(ERROR)

The returned value is duplicated in Status