The wave shape of coherent structure in turbulence can be reconstructed with inverse wavelet transform according to its scale. A new equation

which can more truly reconstruct the amplitude of coherent structure

is presented on the based of the analysis of wavelet transform. Morlet wavelet has a high resolution and can distinguish fundamental wave from subharmonic

however

it can not eliminate the disturbance of high frequency signals. The resolution of orthonormal wavelet is low

but it can eliminate the disturbance of high frequency signals without any other digital filter due to its orthogonality. Therefore

a new equation is presented utilizing the peculiarities of Morlet wavelet and orthonormal wavelet

which is f(x

a)=1H Ψ 1Ψ 2 ∫ +∞ -∞ (W Ψ 1 f)(b

a) Ψ 2a

b (x)1a d b

where a=a m

Ψ 1 is Morlet wavelet

Ψ 2 is a orthonormal wavelet. This equation can not only reconstruct the wave shape of subharmonic

but also overcome the interference of high frequency noise. Based on the character of wavelet analysis

a research method of local singularity of coherent structure is presented. In this method

local intermittency measure of a orthonormal wavelet at coherent structure scale is used to determine the position of a singularity in the coherent structure

and the Mexican hat wavelet modulus at the neighborhood of half the scale of coherent structure is used to calculate every exponent. At last all exponents are averaged by α= ?α(x i)? i . This algorithm can calculate the structure exponent of coherent structure in turbulence. The conclusions are validated with simulative signal and the results show that the reconstruction equation can be used to truly reconstruct the wave shape and amplitude of coherent structure and be used to calculate the structure exponents of coherent structure

though there is strong disturbance of high frequency signals. At last

the conclusions are validated with three-dimensional fluctuation velocities of a round jet flow near the nozzle exit. The results show that the structure exponent of coherent structure is about 1.6.