QccWAVWaveletAnalysis1DInt.3

NAME

QccWAVWaveletAnalysis1DInt, QccWAVWaveletSynthesis1DInt - integer-valued wavelet analysis/synthesis of a 1D signal

int QccWAVWaveletAnalysis1DInt(QccVectorInt signal, int signal_length, int phase, const QccWAVWavelet *wavelet);
int QccWAVWaveletSynthesis1DInt(QccVectorInt signal, int signal_length, int phase, const QccWAVWavelet *wavelet);

DESCRIPTION

QccWAVWaveletAnalysis1DInt() performs one level of an integer-valued wavelet decomposition for a one-dimensional signal. Essentially, QccWAVWaveletAnalysis1DInt() calls QccWAVLiftingAnalysisInt(3) . phase indicates whether signal is to start with an odd- or even-indexed sample; that is, whether odd- or even-phase subsampling is employed after filtering. phase can be either QCCWAVWAVELET_PHASE_EVEN or QCCWAVWAVELET_PHASE_ODD. Additionally, signal_length can be even or odd. wavelet must indicate an integer-valued lifting scheme (see QccWAVLiftingSchemeInteger(3) ).

QccWAVWaveletSynthesis1DInt() performs one level of wavelet synthesis. The first half of signal is assumed to contain the lowpass subband while the second half contains the highpass subband. QccWAVWaveletSynthesis1DInt() calls QccWAVLiftingSynthesisInt(3) . phase indicates whether signal is to start with an odd- or even-indexed sample. signal_length can be even or odd.

Note: In general, you will probably want to use QccWAVWaveletDWT1DInt(3) and QccWAVWaveletInverseDWT1DInt(3) instead of these routines for implementing a discrete wavelet transform and its inverse since QccWAVWaveletDWT1DInt(3) and QccWAVWaveletInverseDWT1DInt(3) allow any number of scales, or levels, of decomposition to be performed.

INTEGER-TO-INTEGER WAVELET TRANSFORMS

Transforms generally provide perfect reconstruction in that the inverse transform will perfectly invert transform coefficients into an exact representation of the original signal. However, when implemented in floating-point arithmetic, the potential for loss arises due to the limits of finite precision in both the forward and inverse transforms. On the other hand, transforms that map integer-valued signals into integer-valued transforms coefficients can guarantee perfect reconstruction, provided an inverse transform can be found. For this reason, lifting schemes, in which inverse transforms are trivial, are favored for the implementation of integer-valued wavelet transforms. Typically, the general approach proposed by Calderbank et al. is followed wherein rounding of floating-point values to integers is performed at each prediction and update step in a lifting scheme. Integer versions of several popular biorthogonal wavelets were created in this manner by Calderbank et al., as well as by Xiong et al.

In traditional floating-point lifting, the prediction and update steps are generally followed by a single application of scaling by a constant in order to produce the usual unitary normalization. This scaling step is somewhat problematic for integer-valued lifting since the scaling constant is usually not an integer. In applications wherein unitary scaling is not required (e.g., in some applications that process each subband completely independently), the scaling step is simply dropped in order to implement an integer-valued version of the transform. Alternatively, one can append three additional lifting steps to implement the scaling; these additional lifting steps can then be rendered integer-valued via appropriate rounding (e.g., Xiong et al.) making the transforms approximately normalized. This latter approach of scaling via additional lifting steps is employed in the integer-valued lifting schemes implemented in QccPack.

RETURN VALUES

These routines return 0 on success and 1 on error.

AUTHOR

Table of Contents

NAME
SYNOPSIS
DESCRIPTION
INTEGER-TO-INTEGER WAVELET TRANSFORMS
RETURN VALUES
SEE ALSO
AUTHOR

NAME

SYNOPSIS

DESCRIPTION

INTEGER-TO-INTEGER WAVELET TRANSFORMS

RETURN VALUES

SEE ALSO

AUTHOR