Signal Processing - Study Mode
[#286] Consider a single input single output discrete-time system with x[n] as input and y[n] as output, where the two are related as $$yleft[ n
ight] = left{ {matrix{
{nleft| {xleft[ n
ight]}
ight|,} & {{
m{for}},0 le n le 10} cr
{xleft[ n
ight] - xleft[ {n - 1}
ight],} & {{
m{otherwise}}} cr
} }
ight.$$ Which one of the following statements is true about the system?
Correct Answer
(A) It is causal and stable
[#287] The z-transform of a system is $$Hleft( z
ight) = {z over {z - 0.2}}.$$ xa0 xa0If the ROC is |z| < 0.2, then the impulse response of the system is
Correct Answer
(D) -(0.2) n u[- n - 1]
[#288] The Dirac-delta function δ(t) is defined as
Correct Answer
(D) $$delta left( t
ight) = left{ {matrix{
{infty ,} & {t = 0} cr
{0,} & {{
m{otherwise}}} cr
} }
ight.,,{
m{and}},intlimits_{ - infty }^infty {delta left( t
ight)dt = 1} $$
[#289] Let h(t) be the impulse response of a linear time invariant system. Then the response of the system for any input u(t) is
Correct Answer
(A) $$intlimits_0^t {hleft( au
ight)} uleft( {t - au }
ight)d au $$
[#290] The response of an initially relaxed linear constant parameter network to a unit impulse applied at t = 0 is 4e -2t u(t). The response of this network to a unit step function will be
Correct Answer
(A) 2[1 - e -2t ]u(t)