A continuous-time system that is initially at rest is described by

$${{dy(t)} \over {dt}} + 3y(t) = 2x(t)$$,

where $$x(t)$$ is the input voltage and $$y(t)$$ is the output voltage. The impulse response of the system is

The Fourier transform $$X(\omega)$$ of the signal $$x(t)$$ is given by

$$X(\omega ) = 1$$, for $$|\omega | < {W_0}$$

$$ = 0$$, for $$|\omega | > {W_0}$$

Which one of the following statements is true?

The Z-transform of a discrete signal $$x[n]$$ is

$$X(z) = {{4z} \over {(z - {1 \over 5})(z - {2 \over 3})(z - 3)}}$$ with $$ROC = R$$.

Which one of the following statements is true?

Which of the following statement(s) is/are true?