The value of $$\int_{-\infty}^{+\infty}e^{-t}\partial\left(2t-2\right)dt$$. where $$\partial\left(t\right)$$ is the Dirac delta function, is

A moving average function is given by $$y\left(t\right)=\frac1T\int_{t-T}^tu\left(\tau\right)d\tau$$. If the input u is a sinusoidal signal of frequency $$\frac1{2T}Hz$$, then in steady state, the output y will lag u (in degree) by ________.

For a periodic signal the $$v\left(t\right)=30\sin100t\;+\;10\cos300t\;+\;6\sin\left(500t\;+\;\frac{\mathrm\pi}4\right)$$ fundamental frequency in radians/s is

A point Z has been plotted in the complex plane, as shown in figure below. The plot of the complex number $$y=\frac1z$$ is