ウィグナー分布
If y ( t ) = a x ( a t ) for some a > 0 then then W y ( t , f ) = W x ( a t , f a ) {\displaystyle {\begin{aligned}{\text{If }}y(t)&={\sqrt {a}}x(at){\text{ for some }}a>0{\text{ then }}\\{\text{then }}W_{y}(t,f)&=W_{x}(at,{\frac {f}{a}})\end{aligned}}}
ウィグナー分布関数には、以下のような特徴的性質がある。
If x ( t ) = 0 for t > t 0 then W x ( t , f ) = 0 for t > t 0 If x ( t ) = 0 for t < t 0 then W x ( t , f ) = 0 for t < t 0 {\displaystyle {\begin{aligned}{\text{If }}x(t)&=0{\text{ for }}t>t_{0}{\text{ then }}W_{x}(t,f)=0{\text{ for }}t>t_{0}\\{\text{If }}x(t)&=0{\text{ for }}t<t_{0}{\text{ then }}W_{x}(t,f)=0{\text{ for }}t<t_{0}\end{aligned}}}