The 3 - dB bandwidth of the low - pass signal $${e^{ - 1}}$$ u(t), where u(t) is the unit step function, is given by

Consider the signal x(t) shown in Fig. Let h(t) denote the impulse response of the filter matched to x(t), with h(t) being non-zero only in the interval 0 to 4 sec. The slope of h(t) in the interval 3 < t < 4 sec is

A system has poles at 0.01 Hz, 1 Hz and 80 Hz; zeros at 5 Hz, 100 Hz and 200 Hz. The approximate phase of the system response at 20 Hz is

The system under consideration is an RC low -pass filter (RC-LPF) with R = 1.0 $$k\Omega $$ and C = 1.0 $$\mu F$$.

Let H(t) denote the frequency response of the RC-LPF. Let $${f_1}$$ be the highest frequency such that $$0 \le \left| f \right| \le {f_1},{{\left| {H({f_1})} \right|} \over {H(0)}} \ge 0.95$$. Then $${f_1}$$ (in Hz) is