Signal processing

[amp_mcq option1=”$${1 \over 5}{e^{3t}}u\left( { – t} \right) + {1 \over 5}{e^{ – 2t}}u\left( { – t} \right)$$” option2=”$$ – {1 \over 5}{e^{3t}}u\left( { – t} \right) + {1 \over 5}{e^{ – 2t}}u\left( { – t} \right)$$” option3=”$${1 \over 5}{e^{3t}}u\left( { – t} \right) – {1 \over 5}{e^{ – 2t}}u\left( t \right)$$” option4=”$$ – {1 \over 5}{e^{3t}}u\left( { – t} \right) – {1 \over 5}{e^{ – 2t}}u\left( t \right)$$” correct=”option3″]

Detailed SolutionInput x(t) and output y(t) of an LTI system are related by the differential equation y”(t) – y'(t) – 6y(t) = x(t). If the system is neither causal nor stable, the impulse response h(t) of the system is

[amp_mcq option1=”Dc term” option2=”Cosine terms” option3=”Sine terms” option4=”Odd harmonic terms” correct=”option4″]

Detailed SolutionThe trigonometric Fourier series of an even function does not have the

[amp_mcq option1=”{-4 – j2.5, j2, 4 – j2.5}” option2=”{-j2.5, 1, j2.5}” option3=”{-j5, j2, 0}” option4=”{-4, 1, 4}” correct=”option1″]

Detailed SolutionConsider the sequence x[n] = {-4 – j5, 1 + j2, 4} The conjugate antisymmetric part of the sequence is

[amp_mcq option1=”sF(s) – f(0)” option2=”$${1 \over s}F\left( s \right)$$” option3=”$$\int\limits_0^s {F\left( \tau \right)} d\tau $$” option4=”$${1 \over s}\left[ {F\left( s \right) – f\left( 0 \right)} \right]$$” correct=”option4″]

Detailed SolutionGiven that F(s) is the one-sided Laplace transform of f(t), the Laplace transform of $$\int\limits_0^t {f\left( \tau \right)} d\tau $$ is