Signal Processing - Study Mode
[#241] The impulse response h(t) of a linear time invariant continuous time system is described by h(t) = exp(αt)u(t) + exp(βt)u(-t) where u(-t) denotes the unit step function, and α and β are real constants. This system is stable if
Correct Answer
(B) α is negative and β is positive
[#242] A linear phase channel with phase delay T p and group delay T g must have
Correct Answer
(A) T p = T g = constant
(H) T p α f and t g = constant (f denotes frequency)
[#243] A signal x(t) = sinc(αt), where α is a real constant, is the input to a linear time invariant system whose impulse response is h(t) = sinc(βt), where β is a real constant. If min(α, β) denotes the minimum of α and β and similarly, max(α, β) denotes the maximum of α and β, and K is a constant, which one of the following statements is true about the $$left( {{ ext{here, }}sin { ext{c}}left( { ext{x}}
ight) = frac{{sin left( {pi { ext{x}}}
ight)}}{{pi { ext{x}}}}}
ight)$$ xa0 xa0 output of the system?
Correct Answer
(A) It will be of the form K sinc(γt) where γ = min(α, β)
[#244] An LTI system having transfer function $$frac{{{s^2} + 1}}{{{s^2} + 2s + 1}}$$ xa0 and input x(t) = sin(t + 1) is in steady state. The output is sampled at a rate ω s rad/s to obtain the final output {y(k)}. Which of the following is true?
Correct Answer
(A) y is zero for all sampling frequencies ω s
(E) y is zero for all sampling frequencies ω s
[#245] Which one of the following must be satisfied if a signal is to be periodic for -∞ < t < ∞?
Correct Answer
(A) x(t + T 0 ) = x(t)