A sinsoidal signal, v(t) = A sin(t), is applied to an ideal full-wave rectifier. Show that the Laplace Transform of the output can be written in the form, $${V_0}\left( s \right) = {A \over {{s^2} + 1}}Coth\left( {\alpha s} \right),$$

where α is a constant. Determine the value of α.

If L$$\left[ {f\left( t \right)} \right]$$ = $${{2\left( {s + 1} \right)} \over {{s^2} + 2s + 5}}$$, then $$f\left( {0 + } \right)\,$$ and $$f\left( \infty \right)$$ are given by

Match each of the items, A, B and C, with an appropriate item from 1, 2, 3, 4 and 5

A. Fourier transform of a Gaussian function
B. Convolution of a rectangular pulse with itself
C. Current through an inductor for a step input voltage

1. Gaussian function
2. Rectangular pulse
3. Triangular pulse Ramp function
4. Rump function
5. Zero