Exams › GATE › Technical

Two discrete-time linear time-invariant systems have impulse responses h1[n] = δ[n−1] + δ[n+1] and h2[n] = δ[n−1] + δ[n+1], where δ[n] is the Kronecker delta. The overall system is

1. δ[n−2] + δ[n+2]
2. δ[n−1]δ[n] + δ[n+1]δ[n−1]
3. δ[n−2] + 2δ[n] + δ[n+2]
4. δ[n−1] + δ[n+1]

Correct answer: δ[n−2] + 2δ[n] + δ[n+2]

Solution

The correct option combines the effects of both impulse responses through convolution, resulting in the sum of shifted delta functions. Each impulse response contributes to the overall system output, leading to the presence of the central term with a coefficient of 2, indicating that the system amplifies the response at n=0.

Related GATE Technical questions

• If the input x(t) and output y(t) of a system are related as y(t) = max(0, x(t)), then the system is
• Consider a power system consisting of N number of buses. Buses in this power system are categorized into slack bus, PV buses and PQ buses for load flow study. The number of PQ buses is N_L. The balanced Newton-Raphson method is used to carry out load flow study in polar form. H, S, M, and R are sub-matrices of the Jacobian matrix J as shown below: [ΔP] [ΔQ] = J [Δδ] [ΔV], where J = [H S M R] The dimension of the sub-matrix M is
• Inductance is measured by
• In the Nyquist plot of the open-loop transfer function G(s)H(s) = (3s + 5)/(s - 1) corresponding to the feedback loop shown in the figure, the infinite semi-circular arc of the Nyquist contour in s-plane is mapped into a point at
• Consider a unity-gain negative feedback system consisting of the plant G(s) (given below) and a proportional-integral controller. Let the proportional gain and integral gain be 3 and 1, respectively. For a unit step reference input, the final values of the controller output and the plant output, respectively, are G(s) = 1/(s - 1)
• The following columns present various modes of induction machine operation and the ranges of slip A Mode of operation a. Running in generator mode b. Running in motor mode c. Plugging in motor mode B Range of Slip p) From 0.0 to 1.0 q) From 1.0 to 2.0 r) From -1.0 to 0.0 The correct matching between the elements in column A with those of column B is

⚔️ Practice GATE Technical free + battle 1v1 →