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Does mixing brown noise and white noise create pink noise?
No.
Pink noise has a spectrum of that falls with 3dB/octave (or 10dB/decade). The spectrum of the sum of white and brown noise will be "brown" at low frequencies and "white" at high frequencies. The spectrum will have two slopes: below the transition frequency it will be -6dB/octave and above it, ...
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Okay, when discussing white noise or pink noise (or red noise or brown noise or flicker) or some other random process, there is this property called the power spectrum, in which white noise has a constant value for all frequencies. But we integrate the power spectrum over all frequencies (from $-\infty$ to $+\infty$) to get power. Integrating a constant, ...
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Wavelets, as bases or frames, are linear like-decompositions. As such, signals and processes can be decomposed into a linear or weighed sum of coefficients multipling (wavelet) vectors:
$$s[n] = \sum a_n e[n]$$
The indexing above is not wavelet-specific. Traditionally, there was some natural order: low $n$ denoting low-scales, or high frequencies, and vice-...
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