Could you tell me why wavelets without scaling functions can't be used for two-dimensional analysis? What is the role of scaling function?

  • $\begingroup$ Please tell what kind of wavelet transform you are thinking of. Continuous, discretized continuous, discrete or fast discrete? And real or complex valued? Why not also framelets, ridgelets or bandelets? $\endgroup$ – Dr. Lutz Lehmann Jan 10 '14 at 14:44

,,A wavelet'' actually is two functions that are orthogonal to each other. That way, a signal can be split into two parts. One part is the wavelet proper, while the other is usually called ,,scaling function'' (sometimes ,,mother wavelet'' as well). When you have just one of both, you can not perform a meaningful wavelet transform.

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    $\begingroup$ If I am not wrong the scaling function is called father wavelet and the detail function mother wavelet $\endgroup$ – Barnaby May 23 '15 at 9:19

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