signal energy

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

An analog pulse s(t) is transmitted over an additive white Gaussian noise (AWGN) channel. The received signal is r(t) = s(t) + n(t), where n(t) is additive white Gaussian noise wit...

Two sequence $${x_1}\left[ n \right]$$ and $${x_2}\left[ n \right]$$ have the same energy. Suppose $${x_1}\left[ n \right]$$ $$ = \alpha \,{0.5^n}\,u\left[ n \right],$$ where $$\al...

The value of the integral $$\int\limits_{ - \infty }^\infty {\sin \,{c^2}} $$ (5t) dt is

If a signal f(t) has energy E, the energy of the signal f(2t) is equal to

The input to a matched filter is given by $$s(t) = \left\{ {\matrix{ {10\sin (2\pi \times {{10}^6}t),} & {0 < \left| t \right| < {{10}^{ - 4}}\sec } \cr 0 & {Otherwise} \cr } } \ri...

The input to a matched filter is given by $$$S\left( t \right) = \left\{ {\matrix{ {10\sin \left( {2\pi \times {{10}^6}t} \right),} & {0 < 1 < {{10}^{ - 4}}\sec } \cr {0\,\,\,\,\,\...

A signal x(t) = $$\exp ( - 2\pi Bt)\,u(t)$$ is the input to an ideal low pass filter with bandwidth B Hz. The output is denoted by y(t). Evaluate $$\int\limits_{ - \infty }^\infty...