Signal Processing MCQ Questions & Answers | ECE

A first-order low-pass filter of time constant T is excited with different input signals (with zero initial conditions up to t = 0). Match the excitation signals X, V, Z with the corresponding time responses for t ≥ 0:
Match List-I with List-II and select the correct answer:

List-I	List-II
X. Impulse	P. $$1 - {e^{ - {t \over T}}}$$
Y. Unit step	Q. $$t - T\left( {1 - {e^{ - {t \over T}}}} \right)$$
Z. Ramp	R. $${e^{ - {t \over T}}}$$

The transfer function of a discrete time LTI system is given by
$$H\left( z \right) = {{2 - {3 \over 4}{z^{ - 1}}} \over {1 - {3 \over 4}{z^{ - 1}} + {1 \over 8}{z^{ - 2}}}}$$
Consider the following statements:
S₁ : The system is stable and causal for
$$ROC:\left| z \right| > {1 \over 2}$$
S₂ : The system is stable but not causal for
$$ROC:\left| z \right| < {1 \over 4}$$
S₃ : The system is neither stable nor causal for
$$ROC:{1 \over 4} < \left| z \right| < {1 \over 2}$$
Which one of the following statements is valid?

Two systems with impulse responses h₁(t) and h₂(t) are connected in cascade. Then the overall impulse response of the cascaded system is given by

The unilateral Laplace transform of f(t) is $${1 \over {{s^2} + s + 1}}.$$   Which one of the following is the unilateral Laplace transform of g(t) = t.f(t)?

A system with an input x(t) and output y(t) is described by the relation: y(t) = tx(t). This system is

Consider the function f(t) having Laplace transform
$$F\left( s \right) = {{{\omega _0}} \over {{s^2} + \omega _0^2}}{\mathop{\rm Re}\nolimits} \left| s \right| > 0$$
The final value of f(t) would be:

An LTI system with unit sample response
h[n] = 5δ[n] - 7δ[n - 1] + 7δ[n - 3] - 5δ[n - 4] is a

Let $$x\left( n \right) = {\left( {\frac{1}{2}} \right)^n}u\left( n \right),y\left( n \right) = {x^2}\left( n \right)$$       and y(e^jω) be the Fourier transform of y(n). Then Y(e^j0) is

Flat top sampling of low pass signals

The region of convergence of z-transform of the sequence
$${\left( {{5 \over 6}} \right)^n}u\left( n \right) - {\left( {{6 \over 5}} \right)^n}u\left( { - n - 1} \right)$$      must be