9.9 Given the first-order transfer function
\frac{0.6}{0.25s + 1}
G(s) =
show the following facts:
Problems P-81
a. For low input frequencies ($\omega \approx 0$), the magnitude of the sinusoidal transfer function (in decibels) is a constant that
is equal to $20 \log_{10}(0.6)$ dB.
b. For very high input frequencies, the magnitude (in decibels) is a straight-line asymptote with slope -20 dB/decade
when plotted on a log scale for input frequency $\omega$.
c. The low- and high-frequency asymptotes intersect at the corner frequency $\omega_c = 4$ rad/s.
[Hint: Begin with the sinusoidal transfer function, compute the log magnitude in decibels, and evaluate at limiting
values of $\omega \to 0$ and $\omega \to \infty$.]
