Let $$m(t)$$ be a strictly band-limited signal with bandwidth B and energy E. Assuming $${\omega _0} = 10B$$, the energy in the signal $$m(t)\cos {\omega _0}t$$ is

The Fourier transform $$x(\omega )$$ of $$x(t) = {e^{ - {t^2}}}$$ is

Note : $$\int\limits_{ - \infty }^\infty {{e^{ - {y^2}}}dy = \sqrt \pi } $$

Consider a real-valued base-band signal $x(t)$. band limited to 10 kHz . The Nyquist rate for the signal $y(t)=x(t) \times \left(1+\frac{t}{2}\right)$ is