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Fast Fourier Transforms (FFT)

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.

Author:
Tony Ottosson and Adam Piatyszek
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.


Function Documentation

void itpp::fft const cvec &  in,
cvec &  out
 

Fast Fourier Transform.

Definition at line 499 of file transforms.cpp.

References it_error.

cvec itpp::fft const cvec &  in  ) 
 

Fast Fourier Transform.

Definition at line 531 of file transforms.cpp.

References itpp::fft().

cvec itpp::fft const cvec &  in,
const int  N
 

Fast Fourier Transform, with zero-padding up to size N.

Definition at line 538 of file transforms.cpp.

Referenced by itpp::arma_estimator(), itpp::fft(), itpp::filter_spectrum(), itpp::freqz(), itpp::spectrum(), and itpp::xcorr().

void itpp::ifft const cvec &  in,
cvec &  out
 

Inverse Fast Fourier Transform.

Definition at line 504 of file transforms.cpp.

References it_error.

cvec itpp::ifft const cvec &  in  ) 
 

Inverse Fast Fourier Transform.

Definition at line 547 of file transforms.cpp.

References itpp::ifft().

cvec itpp::ifft const cvec &  in,
const int  N
 

Inverse Fast Fourier Transform, with zero-padding up to size N.

Definition at line 554 of file transforms.cpp.

Referenced by itpp::arma_estimator(), itpp::ifft(), and itpp::xcorr().

void itpp::fft_real const vec &  in,
cvec &  out
 

Real Fast Fourier Transform.

Definition at line 509 of file transforms.cpp.

References it_error.

cvec itpp::fft_real const vec &  in  ) 
 

Real Fast Fourier Transform.

Definition at line 563 of file transforms.cpp.

References itpp::fft_real().

cvec itpp::fft_real const vec &  in,
const int  N
 

Real Fast Fourier Transform, with zero-padding up to size N.

Definition at line 570 of file transforms.cpp.

Referenced by itpp::arma_estimator(), itpp::fft_real(), and itpp::freqz().

void itpp::ifft_real const cvec &  in,
vec &  out
 

Inverse Real Fast Fourier Transform. Assumes even size.

Definition at line 514 of file transforms.cpp.

References it_error.

vec itpp::ifft_real const cvec &  in  ) 
 

Inverse Real Fast Fourier Transform. Assumes even size.

Definition at line 579 of file transforms.cpp.

References itpp::ifft_real().

vec itpp::ifft_real const cvec &  in,
const int  N
 

Inverse Real Fast Fourier Transform, with zero-padding up to size N.

Definition at line 586 of file transforms.cpp.

Referenced by itpp::filter_design_autocorrelation(), and itpp::ifft_real().

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