GATE Signals and Systems: Applications of Fourier Transform for continuous and discrete time signals, Laplace Transform and Z transform – Previous Year Questions
23 GATE previous year questions on Applications of Fourier Transform for continuous and discrete time signals, Laplace Transform and Z transform (Signals and Systems, Electrical Engineering) with answers and explanations, from every paper.
- GATE 2017 EE Q40 – Let a causal LTI system be characterized by the following differential equation, with initial rest condition d2ydt2 + 7dydt + 10y(t) = 4x(t) +…
- GATE 2017 EE Q61 – Consider a causal and stable LTI system with rational transfer function H(z), whose corresponding impulse response begins at n = 0. Furthermore, H(1)…
- GATE 2015 EE Q45 – Consider a discrete time signal given by x[n] = (-0.25)n u[n] + (0.5)n u[-n-1] The region of convergence of its Z-transform would be
- GATE 2016 EE Q13 – The Laplace Transform of f(t) = e2t (5t) u(t) is
- GATE 2016 EE Q44 – Suppose x 1(t) and x 2(t) have the Fourier transforms as shown below. [Figure: X 1(j) is real and made of three triangles: height 0.3 over from -1 to…
- GATE 2018 EE Q50 – The Fourier transform of a continuous-time signal x(t) is given by X()=1(10+j)2, -<<, where j=-1 and denotes frequency. Then the value of x(t) at t=1…
- GATE 2019 EE Q11 – The inverse Laplace transform of H(s)=s+3s2+2s+1 for t0 is
- GATE 2020 EE Q13 – Which of the following statements is true about the two sided Laplace transform?
- GATE 2020 EE Q14 – Consider a signal x[n]=(12)n 1[n], where 1[n]=0 if n<0, and 1[n]=1 if n0. The z-transform of x[n-k], k>0 is z-k1-12z-1 with region of convergence…
- GATE 2021 EE Q41 – The causal signal with z-transform z2(z-a)-2 is (u[n] is the unit step signal)
- GATE 2021 EE Q42 – Let f(t) be an even function, i.e. f(-t)=f(t) for all t. Let the Fourier transform of f(t) be defined as F()= -f(t)e-j tdt. Suppose dF()d=- F() for…
- GATE 2021 EE Q53 – Consider a continuous-time signal x(t) defined by x(t)=0 for t >1, and x(t)=1- t for t 1. Let the Fourier transform of x(t) be defined as X()=…
- GATE 2022 EE Q11 – The transfer function of a real system, H(s), is given as: H(s)=As+Bs2+Cs+D, where A,B,C and D are positive constants. This system cannot operate as
- GATE 2022 EE Q37 – An LTI system is shown in the figure where G(s)=100s2+0.1s+100. The steady state output of the system, to the input r(t), is given as y(t)=a+b(10t+).…
- GATE 2022 EE Q47 – Let an input x(t)=2(10 t)+5(15 t)+7(42 t)+4(45 t) is passed through an LTI system having an impulse response, h(t)=2((10 t) t)(40 t). The output of…
- GATE 2023 EE Q18 – The Fourier transform X() of the signal x(t) is given by X()=1, for <W o; \ \ =0, for >W o Which one of the following statements is true?
- GATE 2023 EE Q19 – The Z-transform of a discrete signal x[n] is X(z)=4z(z-15)(z-23)(z-3)with ROC=R. Which one of the following statements is true?
- GATE 2023 EE Q50 – The discrete-time Fourier transform of a signal x[n] is X()=(1+)e-j. Consider that x p[n] is a periodic signal of period N=5 such that x p[n]=x[n],…
- GATE 2024 EE Q16 – If u(t) is the unit step function, then the region of convergence (ROC) of the Laplace transform of the signal x(t)=et2[u(t-1)-u(t-10)] is
- GATE 2024 EE Q33 – Let X() be the Fourier transform of the signal x(t)=e-t4 t,-<t<. The value of the derivative of X() at =0 is (rounded off to 1 decimal place).
- GATE 2024 EE Q39 – If the Z-transform of a finite-duration discrete-time signal x[n] is X(z), then the Z-transform of the signal y[n]=x[2n] is
- GATE 2025 EE Q61 – An ideal low pass filter has frequency response given by H(j)=cases1,& 200\\0,&otherwisecases Let h(t) be its time domain representation. Then h(0)=…
- GATE 2026 EE Q11 – Consider the infinite-length, discrete-time sequence x[n]=0.9 n , where n is an integer. The region of convergence of its Z-transform X(z) is given…