DComplexFFTServer Class Reference

Performs double precision complex fast Fourier transforms (FFTs) of an RWMathVec<DComplex> vector. More...

#include <rw/cfft.h>

Inheritance diagram for DComplexFFTServer:

Public Member Functions
	DComplexFFTServer ()
	DComplexFFTServer (size_t order)
	DComplexFFTServer (const DComplexFFTServer &)
RWMathVec< DComplex >	fourier (const RWMathVec< DComplex > &v)
RWMathVec< DComplex >	ifourier (const RWMathVec< DComplex > &v)
DComplexFFTServer &	operator= (const DComplexFFTServer &v)
size_t	order () const
void	setOrder (size_t N)

Detailed Description

Class DComplexFFTServer performs double precision complex fast Fourier transforms (FFTs) of an RWMathVec<DComplex> vector. The transform of a complex vector is a complex vector; therefore, the server returns a complex vector for either a forward or backward (inverse) transform.

At any given moment, the server is configured to transform a vector of a specified length. This length can be set three ways:

• At construction time.
• With the function setOrder().
• By the server from a supplied vector length.

The last method means that if the vector length changes, the server automatically reconfigures to the new length. Since this is an expensive calculation, it is most efficient to call a server repeatedly for series of the same length. Different FFT servers may be constructed to handle different lengths.

There are no restrictions on the number of points; that is, the number need not be a power of 2.

The Fourier transform calculated is:

\[ A(n) = \displaystyle\sum_{j=0}^{N-1}X(j)exp\left(\frac{-2i \pi nj}{N}\right); \quad n=0, \quad .., \quad N-1 \]

The inverse Fourier transform (IDFT) calculated is:

\[ X(j) = \displaystyle\sum_{n=0}^{N-1}A(n)exp\left(\frac{2i \pi nj}{N}\right); \quad j=0, \quad .., \quad N-1 \]

where A and X are complex. Note that the sum is not normalized; a call to fourier() followed by a call to ifourier() results in the original series multiplied by N.

Synopsis

#include <rw/cfft.h>
DComplexFFTServer dcffts;

Constructor & Destructor Documentation

DComplexFFTServer::DComplexFFTServer

(

)

Constructs a complex FFT server to transform a vector of unspecified length. This length is initialized when the server is used.

DComplexFFTServer::DComplexFFTServer

(

size_t

order

)

Constructs a complex FFT server designed to transform a vector of length order.

DComplexFFTServer::DComplexFFTServer

(

const DComplexFFTServer &

)

Copy constructor. The new server references the old server's data.

Member Function Documentation

RWMathVec<DComplex> DComplexFFTServer::fourier

(

const RWMathVec< DComplex > &

v

)

Returns the forward FFT, as defined above, of a complex vector v. The expression:

DComplexFFTServer  f;
RWMathVec<DComplex>  v;
std::cout  <<  f.fourier(v);

outputs the Fourier transform of v as a complex vector with N points. If the server is not currently configured to the length of v, it reconfigures.

RWMathVec<DComplex> DComplexFFTServer::ifourier

(

const RWMathVec< DComplex > &

v

)

Returns the inverse FFT, as defined above, of a complex vector v. The expression:

DComplexFFTServer  f;
RWMathVec<DComplex>  v;
std::cout  <<  f.fourier(v);

outputs the inverse Fourier transform of v as a complex vector with N points.

DComplexFFTServer& DComplexFFTServer::operator=

(

const DComplexFFTServer &

v

)

Sets self to the same order as v.

size_t DComplexFFTServer::order ( ) const

inline

Returns the order of an FFT server, that is, the vector length it is currently configured to transform.

void DComplexFFTServer::setOrder

(

size_t

N

)

Resets the order of an FFT server to N.