The result of the convolution $$x\left( { - t} \right) * \delta \left( { - t - {t_0}} \right)$$ 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 waveform of a periodic signal x(t) is shown in the figure.

A signal g(t) is defined by $$g(t) = x\left( {{{t - 1} \over 2}} \right)$$.

The average power of g(t) is___________________________.

If $$\log_x\left(\frac57\right)=\frac{-1}3$$, then the value of x is