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QUESTION: 1

The convolution of f(t) with itself is given to be Then what is f(t)?

Solution:

QUESTION: 2

Which one of the following is the impulse response of the system whose step response is given as c(t) = 0.5(1 - e^{-2t}) u(t)?

Solution:

QUESTION: 3

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

Solution:

QUESTION: 4

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

Solution:

QUESTION: 5

If a function f(t) u(t) is shifted to the right side by t_{0}, then the function can be expressed as

Solution:

QUESTION: 6

The impulse response of a causal, linear, time- invariant, continuous time system is h(t). The output y(t) of the same system to an input x(t). Where x(t) = 0 for t < -2 is

Solution:

QUESTION: 7

The unit step response of a system is given by (1 - e^{αt}) u(t), the impulse response is given by

Solution:

QUESTION: 8

Figure I and Figure II, shows the input x(t) to a linear time invariant system and the impulse response h(t) of the system

the output of the system is zero everywhere except for the time interval.

Solution:

QUESTION: 9

A signal f(t) = cos8πt + 0.5cos4πt is instantaneously sampled. The maximum allowable value of sampling interval T_{s} in sec is

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QUESTION: 10

The impulse response. h[n] of a linear time invariant system is given by h[n] = u[n + 3] + u[n - 3] - 2u[n - 7], the above system is

Solution:

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