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QUESTION: 1

Which of the following signals are monotonic in nature?

Solution:

All of the other functions have a periodic element in them, which means the function attains the same value after a period of time, which should not occur for a monotonic function.

QUESTION: 2

What is the period of the following signal, x(t) = sin(18*pi*t + 78 deg)?

Solution:

The signal can be expressed as sin(wt + d), where the time period = 2*pi/w.

QUESTION: 3

Which of the following signals is monotonic?

Solution:

reduces to 1 – 2t, which is a strictly decreasing function.

QUESTION: 4

For the signal, x(t) = log(cos(a*pi*t+d)) for a = 50 Hz, what is the time period of the signal, if periodic?

Solution:

Time period = 2*pi/(50)pi = 1/25 = 0.04s

QUESTION: 5

What are the steady state values of the signals, 1-exp(-t), and 1-k*exp(-k*t)?

Solution:

Consider limit at t tending to infinity, we obtain 1 for both cases.

QUESTION: 6

For a bounded function, is the integral of the function from -infinity to +infinity defined and finite?

Solution:

If the bounded function, is say y = 2, then the integral ceases to hold. Similarly, if it is just the block square function, it is finite. Hence, it depends upon the spread of the signal on either side. If the spread is finite, the integral will be finite.

QUESTION: 7

For the signal x(t) = a – b*exp(-ct), what is the steady state value, and the initial value?

Solution:

Put the limits as t tends to infinity and as t tends to zero.

QUESTION: 8

For a double sided function, which is odd, what will be the integral of the function from -infinity to +infinity equal to?

Solution:

For an odd function, f(-x) = -f(x), thus the integrals will cancel each other, giving zero.

QUESTION: 9

Find where the signal x(t) = 1/(t^{2} – 3t + 2) finds its maximum value between (1.25, 1.75):

Solution:

Differentiate the function for an optima, put it to zero, we will obtain t = 1.5 as the required instant.

QUESTION: 10

Is the signal x(t) = exp(-t)*sin(t) periodic in nature?

Solution:

Though sin(t) is a periodic function, exp(-t) is not a periodic function, thus leading to non-periodicity.

### Classification of Systems, Signal, Electrical Engineering, GATE

Video | 33:43 min

### Classification of Systems, Signal, Electrical Engineering, GATE

Video | 33:43 min

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