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)