oph_gsl_dwt¶

Description¶

Behaviour

It computes the Discrete Wavelet Transform of a measure array. Measures must be OPH_DOUBLE. The number of input elements must be a power of 2.

Output format is the following: (s_{-1,0}, d_{0,0}, d_{1,0}, d_{1,1}, d_{2,0}, ..., d_{j,k}, ..., d_{{J-1,2^{J-1}-1}}), where the first element is the smoothing coefficient s_{-1,0}, followed by the detail coefficients d_{j,k} for all levels j=0,...,(log2n) - 1 and for all k=0,...,(2^j)-1 (J=log2n).

Considering DWT as a bank of cascading filters, the last output level corresponds to the ‘Level 1’ containing a number of coefficients equal to half of the input dimension and is related to the sub-band fn/2 – fn. The second-last one corresponds to the ‘Level 2’ with one fourth of the coefficients and related to the sub-band fn/4 – fn/2 and so on. The smoothing coefficient corresponds to the same level of the second output coefficient. If this level is, for example, the number 5, then the second coefficient is the detail coefficient of level 5 (obtained with a high-pass filter) and the first one is the approximation coefficient (obtained with a low-pass filter).

Parameters

• input measure type: Ophidia typing. Supported type is ‘oph_double’.
• input measure type: Ophidia typing. Supported type is ‘oph_double’.
• measure: input measure.
• wavelet family: family of the mother wavelet
  • ‘DAUBECHIES’: Daubechies wavelet (default);
  • ‘DAUBECHIES_C’: centered version of the Daubechies wavelet (sub-bands aligned at edges);
  • ‘HAAR’: Haar wavelet;
  • ‘HAAR_C’: centered version of the Haar wavelet (sub-bands aligned at edges);
  • ‘BSPLINE’: the biorthogonal B-spline wavelet family of order (i,j);
  • ‘BSPLINE_C’: centered version of the biorthogonal B-spline wavelet family of order (i,j) (sub-bands aligned at edges).
• wavelet member: particular instance of the mother wavelet family (k)
  • In case of DAUBECHIES, k=4 (default), 6, ..., 20, with k even;
  • In case of HAAR, k=2 (default);
  • In case of BSPLINE, k = 100* i+j = 103 (default), 105, 202, 204, 206, 208, 301, 303, 305 307, 309.

Return type

Binary-array.

Examples

Compute the coefficients of the Discrete Wavelet Transform of the input array with the Daubechies mother wavelet with 2 vanishing moments.

oph_gsl_dwt('OPH_DOUBLE','OPH_DOUBLE',measure,'DAUBECHIES',4)

Operation type

Simple.

Arguments¶