njit-etd2003-081 - New Jersey Institute of Technology

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where 8(.) is a Dirac delta function. The above equation implies that the energy of the
time-frequency distribution is concentrated along the instantaneous frequency of the
signal. A dual quantity is the average time of a signal at a given frequency. This
quantity is called the group delay. For a signal of the form:
the group delay is defined as:
3. Dr. Leon Cohen has proposed a simple procedure to mathematically
formulate the general class of time-frequency representations using bilinear distributions
[69]:
The g(v,r) is an arbitrary function called the kernel and it determines the
characteristics of the time-frequency distribution. Note that z is an analytic signal and
z* is the complex conjugate of z. Integrating equation (3.13) with respect to v, one
gets: