Starting with the construction conditions of basic wavelet (or mother wavelet)

three topics are studied in this paper.Firstly

the numerical computation stability of dyadic wavelets is discussed with a new concept——the stableness

which enables us to measure the stabilizing ability in numerical inverse of wavelet;And then the stableness of a novel class of complex analytic wavelet——Y-wavelet (whose quality factor is changeable)is analyzed.Finally

we investigate the orthogonal condition of Y-wavelet.Theoretical analysis and results of numerical simulation show that:The stableness and frequency selectivity of wavelets contradict each other in wavelet analysis

but this problem can be mitigated to some extent by changing the scaling dilation parameter;The stability region of dyadic Y-wavelet class is very narrow and limited by larger quality factor;It is impossible to construct an integral translation orthogonal basis by using Y-wavelets

except that the real Y-wavelet might exist on some integral translation orthogonal basis.