A definition for the instantaneous frequency was given in Eq. (2.49). A more general definition is \(f_{i}(t)=\frac{1}{2 \pi} \operatorname{Im}\left\{\frac{d}{d t} \ln \psi(t)ight\}\) where \(\operatorname{Im}\) \{.\}, indicates imaginary part and \(\psi(t)\) is the analytic signal. Using this definition, calculate the instantaneous frequency for
\[
x(t)=\operatorname{Rect}\left(\frac{t}{\tau}ight) \cos \left(2 \pi f_{0} t+\frac{B}{2 \tau} t^{2}ight)
\]

Equation (2.49)

Transcribed Image Text:

f(t)=- 1 d -(t)=fo-ut 2 dt -Tosts 2