Fast Fourier Transform (FFT)
[Transforms]

One dimensional fast fourier transform. More...

Functions
void	itpp::fft (const cvec &in, cvec &out)
	Fast Fourier Transform.
cvec	itpp::fft (const cvec &in)
	Fast Fourier Transform.
cvec	itpp::fft (const cvec &in, const int N)
	Fast Fourier Transform, with zero-padding up to size N.
void	itpp::ifft (const cvec &in, cvec &out)
	Inverse Fast Fourier Transform.
cvec	itpp::ifft (const cvec &in)
	Inverse Fast Fourier Transform.
cvec	itpp::ifft (const cvec &in, const int N)
	Inverse Fast Fourier Transform, with zero-padding up to size N.
void	itpp::fft_real (const vec &in, cvec &out)
	Real Fast Fourier Transform.
cvec	itpp::fft_real (const vec &in)
	Real Fast Fourier Transform.
cvec	itpp::fft_real (const vec &in, const int N)
	Real Fast Fourier Transform, with zero-padding up to size N.
void	itpp::ifft_real (const cvec &in, vec &out)
	Inverse Real Fast Fourier Transform. Assumes even size.
vec	itpp::ifft_real (const cvec &in)
	Inverse Real Fast Fourier Transform. Assumes even size.
vec	itpp::ifft_real (const cvec &in, const int N)
	Inverse Real Fast Fourier Transform, with zero-padding up to size N.

Detailed Description

One dimensional fast fourier transform.

The functions

 X = fft(x)

and

 x = ifft(X)

are the fourier and inverse fourier transforms of size N defined as:

$X(k) = \sum_{j=0}^{N-1} x(j) e^{-2\pi j k \cdot i / N}$

$x(j) = \frac{1}{N} \sum_{k=0}^{N-1} X(k) e^{2\pi j k \cdot i / N}$

 Y = fft(X, N)

performs zero-padding up to size N and then performs an N-size fft.

The implementation is built upon one of the following libraries:

Note:: FFTW-based implementation is the fastest for powers of two. Furthermore, the second time you call the routine with the same size, the calculation is much faster due to many things were calculated and stored the first time the routine was called.; Achieving maximum runtime efficiency with the FFTW library on some computer architectures requires that data are stored in the memory with a special alignment (to 16-byte boundaries). The IT++ memory management functions and container classes do not generally allocate memory aligned this way, and as a result calling FFTW via the IT++ interface (i.e. the fft() function) may be slower than using the FFTW library directly. Therefore, FFTW users concerned about maximum possible performance may want to consider the possibility of calling the FFTW library and its memory management/allocation routines directly, bypassing the IT++ storage classes and the fft() interface to FFTW.