GATE EE 2018 Question Paper (10-Feb-2018) (Shift 2)

Which one of the following statements is true about the digital circuit shown in the figure?

Digital input signals A, B, C with A as the MSB and C as the LSB are used to realize the Boolean function F = m₀ + m₂ + m₃ + m₅ + m₇, where mᵢ denotes the i${}^{th}$ minterm. In addition, F has a don’t care for m₁. The simplified expression for F is given by:

Consider the two continuous-time signals defined below:

x_1≤ft( t ) = ≤ft\{ {*20c ≤ft| t |, - 1 ≤ t ≤ 1 \\ 0, otherwise ,} .x_2≤ft( t ) = ≤ft\{ {*20c 1 - ≤ft| t |, - 1 ≤ t ≤ 1 \\ 0, otherwise } .

These signals are sampled with a sampling period of T = 0.25 seconds to obtain discrete time signals x₁[n] and x₂[n], respectively. Which one of the following statements is true?

The signal energy of the continuous-time signal

X(t) = [(t – 1) u(t - 1)] – [(t - 2)u(t - 2)] – [(t - 3)u(t – 3)] + [(t - 4)]u(t – 4)] is

The Fourier transform of a continuous-time signal x(t) is given by $X\left(\omega \right)=\frac{1}{{\left(10+j\omega \right)}^2},-\infty <\omega <\infty ,$ where $j=\sqrt{-1}$ and ω denotes frequency. Then the value of |ln x(t)| at t = 1 is _____ (up to 1 decimal place). (In denotes the logarithm to base e)