One dimensional Dicrete Cosine Transform. More...

Functions
ITPP_EXPORT bool	itpp::have_cosine_transforms ()
	Run-time test if library is built with cosine transforms enabled.

ITPP_EXPORT void	itpp::dct (const vec &in, vec &out)
	Discrete Cosine Transform (DCT)

ITPP_EXPORT vec	itpp::dct (const vec &in)
	Discrete Cosine Transform (DCT)

ITPP_EXPORT vec	itpp::dct (const vec &in, const int N)
	Discrete Cosine Transform (DCT) with zero-padding up to size N.

ITPP_EXPORT void	itpp::idct (const vec &in, vec &out)
	Inverse Discrete Cosine Transform (IDCT)

ITPP_EXPORT vec	itpp::idct (const vec &in)
	Inverse Discrete Cosine Transform (IDCT)

ITPP_EXPORT vec	itpp::idct (const vec &in, const int N)
	Inverse Discrete Cosine Transform (IDCT) with zero-padding up to size N.

Detailed Description

One dimensional Dicrete Cosine Transform.

The functions

X = dct(x)

and

x = idct(X)

are the dicrete cosine and inverse discrete cosine transforms of size N defined as:

$X(k) = w(k) \sum_{j=0}^{N-1} x(j) \cos \left(\frac{(2j+1)k \pi}{2N} \right)$

$x(j) = \sum_{k=0}^{N-1} w(k) X(k) \cos \left(\frac{(2j+1)k \pi}{2N} \right)$

where $w(k) = 1/sqrt{N}$ for $k=0$ and $w(k) = sqrt{2/N}$ for $k\geq 1$ .

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 dct()/idct() 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 dct()/idct() interface to FFTW.

Function Documentation

Discrete Cosine Transform (DCT) with zero-padding up to size N.

First N points of input vector are used to perform the transform if N < length(in). Padding with 0's is performed if N > length(in).

Inverse Discrete Cosine Transform (IDCT) with zero-padding up to size N.

First N points of input vector are used to perform the transform if N < length(in). Padding with 0's is performed if N > length(in).