FFT Servers

SourcePro : Essential Math Module User’s Guide : FFT Servers

FFT Servers

Overview

Transforms of Real Sequences

Transforms of Even and Odd Sequences

Overview

Three fast Fourier transform (FFT) servers are included in the Essential Math Module class library:

Class DComplexFFTServer transforms an RWMathVec<DComplex> vector into an RWMathVec<DComplex> and back;

Class DoubleFFTServer transforms a real RWMathVec<double> into a complex conjugate-even vector and back;

Class DComplexFFT2DServer transforms an RWGenMat<DComplex> matrix into an RWGenMat<DComplex> and back.

In addition, a fast sine/cosine transform server is included:

Class DoubleCosineServer can take the sine or cosine transform of a real RWMathVec<double> into a real RWMathVec<double> and back.

The only restriction on the length of a vector that can be transformed is that a real RWMathVec<double> must have an even number of points. In particular, vector lengths need not be a power of 2, although the transform is more efficient if they are. More generally, vectors with lengths that have small prime factors transform the most efficiently. By definition, a power of 2 has prime factors of 2—the smallest of all.

At any given moment, a server is configured to transform a vector of a specified length. The appropriate weights, which are actually the roots of one of the prime factors, are stored internally. This length can be set:

At construction time

By using the member function setOrder()

Dynamically from a vector length, as shown in the following code:

// Will transform vectors 10 points long:

DComplexFFTServer aserv(10);

aserv.setOrder(20); // Now set for 20 points

RWMathVec<DComplex> b(30, rwUninitialized);

// Forward FFT of b:

RWMathVec<DComplex> btrans = aserv.fourier(b);

//aserv would now be set for vectors 30 pts long.

Because reconfiguring for a new vector length is a relatively expensive process, if more than one vector length must be transformed within a program, it is better to build several servers rather than to keep reconfiguring one. This means it is possible to transform efficiently and conveniently more than one vector length within a stretch of code, something that is difficult to do with conventional Fortran-based FFT functions.

See the SourcePro API Reference Guide for a description of the exact transforms that are calculated.