Revision as of 00:57, 13 November 2015 edit RRamakr6 (talk \| contribs) 153 edits →Multidimensional separable Discrete Wavelet Transform (DWT) ← Previous edit		Revision as of 01:11, 13 November 2015 edit undo RRamakr6 (talk \| contribs) 153 edits →Implementation of multidimensional (M-D) dual tree CWT Next edit →
Line 54: {{=}} ψ(x)<sub>h</sub>ψ(y)<sub>h</sub> - ψ(x)<sub>g</sub>ψ(x)<sub>g</sub> + j [ψ(x)<sub>h</sub>ψ(y)<sub>g</sub> - ψ(x)<sub>h</sub>ψ(x)<sub>g</sub>]}} The support of the Fourier spectrum of the wavelet above resides in first quadrant ~~as in the diagram~~. When just the real part is considered, {{math\|Real(ψ(x,y)) {{=}} ψ(x)<sub>h</sub>ψ(y)<sub>h</sub> - ψ(x)<sub>g</sub>ψ(x)<sub>g</sub>}} has support on opposite quadrants (see figure in (a)). Both {{math\|ψ(x)<sub>h</sub>ψ(y)<sub>h</sub>}} and {{math\|ψ(x)<sub>g</sub>ψ(y)<sub>g</sub>}} correspond to HH subband of two different separable 2-D DWTs. This wavelet is oriented at {{math\|-45<sup>o</sup>}}. Similarly, by considering {{math\| ψ<sub>2</sub>(x,y) {{=}} ψ(x)ψ(y)<sup></sup>}}, wavelet oriented at {{math\|45<sup>o</sup>}} is obtained. To obtain 4 more oriented real wavelets, {{math\|φ(x)ψ(y)}}, {{math\|ψ(x)φ(y)}}, {{math\|φ(x)ψ(y)<sup></sup>}} and {{math\|ψ(x)φ(y)<sup>*</sup>}} are considered.

Wavelet for multidimensional signals analysis: Difference between revisions