GATE Signals and Systems: Linear time invariant and causal systems – Previous Year Questions
26 GATE previous year questions on Linear time invariant and causal systems (Signals and Systems, Electrical Engineering) with answers and explanations, from every paper.
- GATE 2017 EE Q13 – Let z(t) = x(t) * y(t), where "*" denotes convolution. Let c be a positive real-valued constant. Choose the correct expression for z(ct).
- GATE 2017 EE Q17 – Consider the system with following input-output relation y[n] = (1 + (-1)n)\,x[n] where x[n] is the input and y[n] is the output. The system is
- GATE 2015 EE Q19 – A moving average function is given by y(t) = 1T t-Tt u()\,d. If the input u is a sinusoidal signal of frequency 12T Hz, then in steady state, the…
- GATE 2015 EE Q20 – The impulse response g(t) of a system, G, is as shown in Figure (a). What is the maximum value attained by the impulse response of two cascaded blocks…
- GATE 2016 EE Q18 – Consider a continuous-time system with input x(t) and output y(t) given by y(t) = x(t) (t) This system is
- GATE 2016 EE Q45 – The output of a continuous-time, linear time-invariant system is denoted by T\x(t)\ where x(t) is the input signal. A signal z(t) is called…
- GATE 2018 EE Q26 – A continuous-time input signal x(t) is an eigenfunction of an LTI system, if the output is
- GATE 2018 EE Q43 – Consider a system governed by the following equations dx 1(t)dt=x 2(t)-x 1(t),dx 2(t)dt=x 1(t)-x 2(t). The initial conditions are such that x 1(0)<x…
- GATE 2019 EE Q17 – The symbols a and T represent positive quantities, and u(t) is the unit step function. Which one of the following impulse responses is NOT the output…
- GATE 2020 EE Q12 – Which of the following is true for all possible non-zero choices of integers m,n;\ m n, or all possible non-zero choices of real numbers p,q;\ p q, as…
- GATE 2020 EE Q47 – Suppose for input x(t) a linear time-invariant system with impulse response h(t) produces output y(t), so that x(t)*h(t)=y(t). Further, if x(t) * h(t)…
- GATE 2020 EE Q49 – Which of the following options is true for a linear time-invariant discrete time system that obeys the difference equation: y[n]-ay[n-1]=b 0x[n]-b…
- GATE 2021 EE Q16 – If the input x(t) and output y(t) of a system are related as y(t)=(0,x(t)), then the system is
- GATE 2021 EE Q17 – Two discrete-time linear time-invariant systems with impulse responses h 1[n]=[n-1]+[n+1] and h 2[n]=[n]+[n-1] are connected in cascade, where [n] is…
- GATE 2022 EE Q46 – Let a causal LTI system be governed by the following differential equation y(t)+14dydt=2x(t), where x(t) and y(t) are the input and output…
- GATE 2022 EE Q48 – Consider the system as shown below where y(t)=x(et). The system is
- GATE 2023 EE Q17 – A continuous-time system that is initially at rest is described by dy(t)dt+3y(t)=2x(t), where x(t) is the input voltage and y(t) is the output…
- GATE 2023 EE Q27 – Which of the following statement(s) is/are true?
- GATE 2023 EE Q31 – For the signals x(t) and y(t) shown in the figure, z(t)=x(t)*y(t) is maximum at t=T 1. Then T 1 in seconds is (Round off to the nearest integer).
- GATE 2023 EE Q36 – The magnitude and phase plots of an LTI system are shown in the figure. The transfer function of the system is
- GATE 2024 EE Q15 – Suppose signal y(t) is obtained by the time-reversal of signal x(t), i.e., y(t)=x(-t), -<t<. Which one of the following options is always true for the…
- GATE 2024 EE Q37 – The input x(t) and the output y(t) of a system are related as y(t)=e-t -te x()\,d,-<t<. The system is
- GATE 2024 EE Q38 – Consider the discrete-time systems T 1 and T 2 defined as follows: \T 1x\[n]=x[0]+x[1]++x[n] \T 2x\[n]=x[0]+12x[1]++12nx[n] Which one of the following…
- GATE 2025 EE Q20 – Consider a discrete-time linear time-invariant (LTI) system S, where y[n]= S\x[n]\. Let S\[n]\=cases1,&n\0,1,2\\\0,&otherwisecases where [n] is the…
- GATE 2025 EE Q40 – Let continuous-time signals x 1(t) and x 2(t) be x 1(t)=cases1,&t[0,1]\\2-t,&t[1,2]\\0,&otherwisecasesand x…
- GATE 2025 EE Q42 – The continuous-time unit impulse signal is applied as an input to a continuous-time linear time-invariant system S. The output is observed to be the…