A Measurement for Real Finite Energy Signal Symmetry
Yong Chen, Yuan Ming Xiao · 2007
This paper focuses on the symmetry of continued-time real signals in spatial domain.The generic definition of a real signal symmetry is given.A symmetric degree function of a real signal is deduced from projection theory and orthogonal-decomposition theory in inner product space is presented.The symmetric degree function shows that the symmetry of a real signal changes with the shift of center symmetric point.Based on the signal symmetric degree function,a quantitative symmetric index of a real signal is obtained.Finally,the symmetry of the classical and least asymmetrical Daubechies scaling function and wavelets are analyzed.These symmetry indices quantitatively confirm the symmetric characters of Daubechies wavelets.