A continuous-time filter with transfer function $$\,H(S) = {{2s + 6} \over {{s^2} + 6s + 8}}$$ is converted to a discrete time filter with transfer function $$G(Z) = {{2{z^2} - 0.5032\,z} \over {{z^2} - 0.5032z + k}}$$ so that the impulse response of the continuous-time filter, sampled at 2 Hz, is identical at the sampling instants to the impulse response of the discrete time filter, The value of k is _________________________.

In the system shown in Figure (a), m(t) is a low-pass signal with bandwidth W Hz. The frequency response of the band-pass filter H(f) is shown in Figure (b). If it is desired that the output signal z(t) = 10x(t), the maximum value of W (in Hz) should be strictly less than ___________________________

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