GATE ECE 1998 | Continuous Time Linear Invariant System Question 40 | Signals and Systems

The unit impulse response of a linear time invariant system is the unit step function u(t). For t>0, the response of the system to an excitation e^-at u(t), a>0 will be

a e^-at

(1/a) (1 - e^-at)

a(1 - e^-at)

1 - e^-at)

GATE ECE 1995

MCQ (Single Correct Answer)

-0.3

Non - minimum phase transfer function is defined as the transfer function

which has zeros in the right - half s - plane.

which has zeros only in the left - half s - plane.

which has poles in the right - half s - plane.

which has poles in the left - half s - plane.

GATE ECE 1995

MCQ (Single Correct Answer)

-0.3

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

$$\int\limits_0^t {h\left( \tau \right)} u\left( {t - \tau } \right)d\tau \,\,\,\,\,\,$$

$${d \over {dt}}\int\limits_0^t {h\left( \tau \right)u\left( {t - \tau } \right)d\tau \,\,\,\,\,} $$

$${\int\limits_0^t {\left[ {\int\limits_0^t {h\left( \tau \right)u\left( {t - \tau } \right)d\tau } } \right]dt\,\,\,\,\,\,} }$$

$${\int\limits_0^t {{h^2}\left( \tau \right)u\left( {t - \tau } \right)d\tau } }$$

GATE ECE 1995

MCQ (Single Correct Answer)

-0.3

The transfer function of a linear system is the

ratio of the output, v₀(t), and input, v_i(t).

ratio of the derivatives of the output and the input.

ratio of the Laplace transform of the output and that of the input with all initial conditions zeros.

none of these.

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