PYQs Based Test - 03 : Signals & Systems

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 of a causal linear time-invariant system?

Consider signal x≤ft( t ) = ≤ft\{ {*20c 1,&≤ft| t | ≤ 2\\ 0,&≤ft| t | > 2 } . Let 𝛿(𝑡) denote the unit impulse (Dirac-delta) function. The value of the integral $\underset{0}{\overset{5}{\int }}2x\left(t-3\right)\delta \left(t-4\right)$ dt is

The input-output relationship of an LTI system is given below.



For an input x[n] shown below



the peak value of the output when x[n] passes through h is ________

Let the signal $x\left(t\right)=\sum _{k=-\infty }^{+\infty }{\left(-1\right)}^k\delta \left(t-\frac{k}{2000}\right)$ be passed through an LTI system with frequency response H(ω), as given in the figure below.



The Fourier series coefficients of the output is given as

If a continuous-time signal x(t) = cos(2πt) is sampled at 4 Hz, the value of the discrete-time sequence x(n) at n = 5 is