Characterization of analytic phase signals

نویسندگان

  • Tao Qian
  • Qiuhui Chen
چکیده

In many cases, a real-valued signal x(t) may be associated with a complex-valued signal a(t)e ~°(t) , the analytic signal associated with x'(t) with the characteristic properties x(t) = a(t) cos O(t) and "H(a(.)cos0(-))(t) = a(t)sin0(t). Using such obtained amplitude-frequency modulation the instantaneous frequency of x(t) at the time to may be defined to be 0'(t0), provided O'(to) >_ O. The pro'pose of this note is to characterize, in terms of analytic functions, the unimodular functions F(t) = C(t)+ iS(t),C2(t)÷ S2(t) = 1, a.e., that satisfy ~C(t) = S(t). This corresponds to the case a(t)-1 in the above formulation. We show that a unimodular function satisfies the required condition if and only if it is the boundary value of a so called inner function in the upper-half complex plane. We also give, through an explicit formula, a large class of functions of which the parametriza-tion C(t) = cos0(t) is available and the extra condition O'(t) >_ 0, a.e. is enjoyed. This class of functions contains Blaschke products in the upper-half complex plane as a proper subclass studied by Picinbono in [1].

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عنوان ژورنال:
  • Computers & Mathematics with Applications

دوره 51  شماره 

صفحات  -

تاریخ انتشار 2006